even continuity and equicontinuity in fuzzy topology we study the notion of even continuity in the category fcs of fuzzy convergence spaces and in fns the category of fuzzy neighborhood spaces we further compare this notion to equicontinuity in fus the category of fuzzy uniform spaces

gibbs sampling for conditional spatial disaggregation of rain fields 1 gibbs sampling is used to simulate sahelian rain fields conditional to an areal estimate provided either as the output of an atmospheric model or by a satellite rainfall algorithm whereas various methods are widely used to generate simulated rain fields conditioned on point observations there are many fewer simulation algorithms able to produce a spatially disaggregated rain field of known averaged value the theoretical and practical aspects of gibbs sampling for the purpose of conditional rain field simulation are explored in the first part of the paper it is proposed to used a so called acceptation rejection algorithm to ensure convergence of the conditional simulation on a sahelian case study it is then showed that gibbs sampling performs similarly to the well known turning band method in an unconditional mode a preliminary validation of the method in conditional mode is presented several rain fields are simulated conditionally on an observed rainfield whose only the spatial average over a 100 100 km2 area is supposed to be known these conditional simulations are compared with the observed rain field and to other rain fields of similar magnitude for a given class of events the conditional rain fields have a distribution of point values similar to the distribution of observed point values at the same time the model is producing a wide range of spatial patterns corresponding to a single area average giving an idea of the variety of possible fields of equal areal value

facilitating the gibbs sampler the gibbs stopper and the griddy gibbs sampler abstract the article briefly reviews the history literature and form of the gibbs sampler an importance sampling device is proposed for converting the output of the gibbs sampler to a sample from the exact posterior this gibbs stopper technique is also useful for assessing convergence of the gibbs sampler for moderate sized problems also presented is an approach for implementing the gibbs sampler in nonconjugate situations the basic idea is to approximate the true cdf of each conditional distribution by a piecewise linear function and then sample from the approximation questions relating to the number of nodes in the approximation gap size between successive nodes and the treatment of unbounded intervals for a given conditional are discussed the methodology is illustrated using a genetic linkage model a nonlinear regression model and the cox model

stratified hutton uniform spaces in this paper some categorical properties of hutton uniform spaces are investigated at first the initial and final structures for hutton uniform spaces are discussed and it is proved that the canonical functor from the construct of hutton uniform spaces to that of l topological spaces preserves initial sources secondly the notion of stratified hutton uniform spaces is introduced and it is demonstrated that every stratified hutton uniformity induces a stratified l topology and that the relationship between stratified hutton uniform spaces and hutton uniform spaces is like that between stratified l topological spaces and l topological spaces finally it is showed that the construct of uniform spaces can be embedded in the construct of stratified hutton uniform spaces as a concretely both reflective and co reflective full sub construct

self avoiding walks that cross a square the authors consider self avoiding walks that traverse an l l square lattice whittington and guttmann 1990 have proved the existence of a phase transition in the infinite l limit at a critical value of the step fugacity they make several finite size scaling predictions for the critical region using the relation between self avoiding walks and the n vector model of magnetism adsorbing as well as nonadsorbing boundaries are considered the predictions are in good agreement with numerical data for l or 9

the categorical topology approach to fuzzy topology and fuzzy convergence it is the purpose of this paper to have a look at fuzzy topology from the point of view of categorical topology we first look at interesting subcategories of fts and determine whether they are bireflective and or coreflective we also describe the set of all subcategories of fts which are at the same time bireflective and coreflective due to the fact that top is one of these subcategories of fts ffs itself can be neither cartesian closed nor extensional we therefore secondly construct a supercategory of bts which is a topological quasitopos the construction of this quasitopos is based on the theory of convergence in fts

metrization theorems in l topological spaces abstract in this paper some characterizations of a pointwise uniformity are presented in l fuzzy set theory a new hausdorff separation axiom compatible with pointwise metric is introduced urysohn metrization theorem and alexandroff urysohn metrization theorem in general topology are generalized to l topology

on regularity axioms in fuzzy neighbourhood spaces abstract two notions of regularity in fuzzy neighbourhood spaces fns s have been introduced one by t m g ahsanullah and the other by the authors we prove that those two notions coincide we then characterize a regular fns as a fns whose level topologies for all 0

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

on fuzzy pseudo metric spaces this paper attempts to endow the fuzzy pseudo metric in the sense of george and veeramani with many valued topological structures it is shown that george and veeramani s fuzzy pseudo metric can be characterized by a family of compatible ordinary pseudo metrics called pseudo metric chain in this paper then two kinds of many valued topological structures fuzzifying topology and fuzzifying uniformity are generated by this fuzzy pseudo metric and their properties are also investigated

transfer matrix study of the adsorption of a flexible self avoiding polymer chain in two dimensions the authors model the polymer as a self avoiding walk on a semi infinite square lattice with an energy contribution in from each step along the lattice boundary the critical adsorption temperature ta and the ordinary and special surface exponents of the walk above and at the adsorption temperature respectively are estimated with transfer matrix finite size scaling methods for the adsorption temperature they obtain exp in kta 2 041 or 0 002 and for the crossover and susceptibility exponents of the special transition phi sp 0 501 or 0 003 and gamma 1sp 1 454 or 0 004

self avoiding walks which cross a square the authors consider self avoiding walks on the square lattice which are confined to lie in or on the boundary of a square with vertices at 0 0 0 l l 0 and l l they ask for the number of such walks which begin at the origin and end at the vertex l l especially in the large l limit similarly they ask for the mean number of steps in such walks as a function of l at fixed l the authors also associate a fugacity with the number of steps of the walk and ask how the system behaves as a function of this fugacity they provide some rigorous results in particular proving that there is a phase transition at some particular value of the fugacity and supplement these with the analysis of series data for the problem

the size and number of rings on the square lattice the authors have calculated the number of self avoiding polygons on the square lattice to 56 steps and the caliper size to 54 steps analysis of the generating function permits estimates of the connective constant mu 2 638 1585 or 10 6 and the critical exponents alpha 0 500 06 or 0 000 06 and v 0 753 or 0 007 the singularity structure of the polygon generating function is found to be consistent with a correction to the scaling exponent delta 1 5 as predicted by nienhuis 1982 1984 the confluent part however maps into the additive analytic term due to the value of the exponent alpha

composite models of polygons a composite polygon is composed of a lattice polygon in the square lattice which contains in its interior an internal structure which may also be a lattice polygon or a lattice tree or a lattice animal or a lattice disc or a collection of these the properties of composite polygons are considered in this manuscript in particular i shall consider the growth constants and generating functions of these models as well as the statistical mechanics of interacting models of composite polygons it is shown that there is an adsorption transition of the internal structure on the containing polygon and a transition which corresponds to the inflation of the containing polygon by the internal structure

regular articlelowen spaces an l fuzzy topological space x is called a lowen space if has a basis consisting of leveled characteristic functions that is to say the elements in of the form au a l u x are a basis for in the case l 0 1 x is a lowen space if and only if x is a fuzzy neighborhood space in the sense of lowen it is proved in this paper that the category of lowen spaces is a simultaneously bireflective and bicoreflective subcategory of the category of l fuzzy topological spaces and it is isomorphic to the category of l fuzzifying topological spaces several characterizations of these spaces are given

fuzzy uniform spaces in this paper we introduce the notion of fuzzy uniform spaces in section 2 we give some basic results and show how a fuzzy topology is derived from a fuzzy uniformity in sections 3 and 4 we prove that the notions which are introduced are good extensions and we prove that the category of uniform spaces is nicely injected in the category of fuzzy uniform spaces finally in section 5 we prove some basic results

critical behaviour of self avoiding walks that cross a square consider the set of all self avoiding walks in the square lattice which start at 0 0 end at l l and are entirely contained in the square 0 l 0 l associate a fugacity x with each step of the walk whittington and guttmann 1990 showed that the dominant walks have o l steps when x is small and o l2 steps when x is large and they conjectured that there is a single transition point at x mu 1 where mu is the inverse of the connective constant for unconstrained self avoiding walks we present a rigorous proof of this conjecture and its analogue in higher dimensions we also discuss what can be said rigorously about two scaling exponents associated with this phase transition and compare this with analogous results that have been obtained exactly and rigorously on the discrete sierpinski gasket by hattori hattori and kusuoka 1990

a theory of fuzzy uniformities with applications to the fuzzy real lines abstract for each completely distributive lattice l with order reversing involution the fuzzy real line r l is uniformizable by a uniformity which both generates the canonical fuzzy topology and induces a pseudometric generating the canonical topology if l is also a chain the usual addition and multiplication defined on r r 0 1 extend jointly fuzzy continuously to and on r l three fundamental questions in fuzzy sets until now are question a if l 1 l 2 is r l 1 uniformly isomorphic to r l 2 in some sense question b for each chain l is jointly uniformly continuous in a sense which guarantees its joint continuity on r l question c is r l a complete pseudometric space in some sense we construct categories qu and u using the quasi uniformities of b hutton which enable us to answer these questions in the affirmative these results enhance the canonical standing of the fuzzy real lines and so give additional justification for answering in the affirmative question d does fuzzy topology have deep specific canonical examples

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the theory of global fuzzy neighborhood structures part i the general case abstract this paper is devoted to global fuzzy neighborhood structures we introduce three types of these structures defined by means of fuzzy filters in some sense the first type is more general than the second one and the second type is more general than the third one in the second case only homogeneous fuzzy filters are used in the third case homogeneous fuzzy filters are used which are representable by a prefilter or equivalently prefilters are used which represent special homogeneous fuzzy filters all fuzzy topologies and stratified fuzzy topologies are global fuzzy neighborhood structures of the first and second type respectively they appear in a canonical way as interior operators fuzzy neighborhood structures introduced by lowen fuzzy sets and systems 7 1982 165 are defined by means of prefilters the definition of these structures is in some sense similar to a characterization of those global fuzzy neighborhood structures of the third type which can be identified with fuzzy topologies however the related fuzzy topological approach differs fuzzy neighborhood structures in sense of lowen are characterized canonically as fuzzy closure operators in this paper the relations between the three types of global fuzzy neighborhood structures and their associated fuzzy topologies and also some relations to the fuzzy neighborhood structures in the sense of lowen are investigated moreover this paper deals with initial and final structures of global fuzzy neighborhood structures in two subsequent papers part ii and part iii fuzzy topogenous orders and fuzzy uniform structures will be investigated respectively all regular fuzzy topogenous orders that is all fuzzy topogenous structures and in particular all fuzzy proximities are global fuzzy neighborhood structures as is shown by examples there exist global fuzzy neighborhood structures which are not fuzzy topogenous structures hence the notion of global fuzzy neighborhood structure is more rich fuzzy uniform structures defined analogously to a weil s definition of a uniform structure as fuzzy filters generate in a canonical way global fuzzy neighborhood structures some results on global fuzzy neighborhood structures will also be published in gahler et al submitted in particular those related to stratifications

on initial and final fuzzy uniform structures this paper is devoted to study the initial and final fuzzy uniform structures of the fuzzy uniform structure defined by the author and others in 1998 in this paper we show that all initial and final lifts in the category fun of these fuzzy uniform spaces and hence the initial and final fuzzy uniform structures exist we introduce a characterization for the initial fuzzy uniform structures and as a special initial fuzzy uniform spaces the subspaces and product spaces of these fuzzy uniform spaces can be also characterized we also show that the fuzzy topology global homogeneous fuzzy neighborhood structure associated to the initial fuzzy uniform structure of a family of fuzzy uniform structures coincides with the initial fuzzy topology initial global homogeneous fuzzy neighborhood structure of the family of fuzzy topologies global homogeneous fuzzy neighborhood structures associated to these fuzzy uniform structures

l uniform spaces versus i l uniform spaces this paper studies relationships between the categories of i l uniform spaces l uniform spaces and uniform spaces we construct two adjunctions f l j l between the category of i l uniform spaces and the category of l uniform spaces and f l j l between the category of l uniform spaces and the category of uniform spaces with l a complete lattice with an order reversing involution in both cases which with l 0 1 and l i 0 1 respectively reduce to the adjunction from the category of i uniform spaces to the category of uniform spaces investigated by katsaras if l is any complete lattice not necessarily with an order reversing involution then so is the l unit interval i l and we have another adjunction viz f i l j i l from the category of i l uniform spaces to the category of uniform spaces we show that the following two factorizations hold f i l f l f l and j i l j l j l when l is a meet continuous lattice with an order reversing involution there is also a natural link between f l j l and the existing adjunction w l i l from the category of i l topological spaces to the one of l topological spaces via the forgetful functors an essential tool in this paper is the theory of galois connections it is emphasized that no kind of distributivity is assumed on the lattice l in this paper

a level topologies criterion for lowen fuzzy uniformizability throughout x will be a nonempty set we consider a subset m of x as a crisp fuzzy set and denote this again by m we denote the strong cut of a fuzzy set e ix by and its weak cut by e i

on fuzzy uniform spaces on donne des resultats sur les espaces flous uniformes on montre que pour toute uniformite u sur un ensemble x correspond une uniformite flou u

the theory of global fuzzy neighborhood structures iii fuzzy uniform structures in this paper a new notion of fuzzy uniform structure is presented and investigated fuzzy uniform structures are given as special fuzzy filters of special interest are those fuzzy uniform structures which are sup fuzzy filters they can be characterized by a related notion of fuzzy syntopogenous structure as is shown fuzzy metrics gahler and gahler 1994 generate fuzzy uniform structures in our sense each fuzzy uniform structure has an associated global homogeneous fuzzy neighborhood structure and hence also an associated fuzzy topology in case of a 0 1 fuzzy uniform structure and even in a more general case a fuzzy uniform structure of the first type can be associated there are given relation to huttons s and katsaras notions of fuzzy uniform structure hutton 1977 katsaras 1979 and to the notion of fuzzy syntopogenous structure in sense of katsaras and petalas 1984

asymptotic behaviour of the number of self avoiding walks on finitely ramified fractals we study self avoiding walks saws on the checkerboard cb family of fractals each member of which can be labelled by an odd integer b 3 or b infinity so that the fractal dimension df tends to the euclidean value 2 when b to infinity by applying the exact renormalization group method for b 3 5 and 7 and the monte carlo renormalization group method for a sequence of fractals with 5 or b or 81 we have calculated the critical exponent gamma associated with the total number of distinct saws it turns out that gamma being always larger than the corresponding euclidean value 43 32 increases monotonically with b in order to learn the asymptotic behaviour of gamma for large b we have applied the finite size scaling fss method based on previous exact results for wedges of the two dimensional euclidean lattices and thereby we have shown that applying the same method fss we have also demonstrated that the critical exponent nu associated with the mean squared end to end distance of saws tends to the euclidean value 3 4 from below when b to infinity the obtained results extend and in a way weld together the previous studies of saws various families of finitely ramified fractals

uniform environments as a general framework for metrics and uniformities this paper puts theories of classical uniformity probabilistic uniformity hutton uniformity classical metric probabilistic metric and hutton metric into one framework by introducing the concept of uniform environment which is a functor from the category of sets to the opposite category of involutive unital quantales and involutive closed unital maps subject to certain conditions the results show that uniform environments and their transformations provide a nice framework to study relationships between various notions of uniformity in the literature

on the category of fixed basis frame valued topological groups this article gives results on fixed basis frame valued neighborhood topological groups and stratified neighborhood topological groups includes some characterization theorems and presents the uniformizability of stratified neighborhood topological groups within the unified approach of gutierrez garcia deprada vicente and sostak it is shown that for a frame l the category l ngrp is topological over grp with respect to the forgetful functor

exact transfer matrix enumeration and critical behaviour of self avoiding walks across finite strips we use a transfer matrix with suitably defined vertex weights to algebraically enumerate n step self avoiding walks confined to cross an l m rectangle on the square lattice we construct the exact generating functions for self avoiding walks from the south west to south east corners for l 1 2 3 4 5 and infinite height m corresponding to a half strip we also consider the number of n sided polygons rooted to the south west corner of the half strip and give a formulation to treat self avoiding walks across the full strip in each case the exact generating functions are ratios of polynomials in the step fugacity we investigate the singularity structure of the generating functions along with the finite size scaling in m of the singularity in the analogue of the heat capacity we find the critical exponents gamma 1 and gamma 2 for the half and open strip along with nu 1 2 these results are indicative of the one dimensional or gaussian nature of self avoiding walks in infinitely long but finitely wide strips

self avoiding walks crossing a square we study a restricted class of self avoiding walks saws which start at the origin 0 0 end at l l and are entirely contained in the square 0 l 0 l on the square lattice z 2 the number of distinct walks is known to grow as l 2 o l 2 we estimate 1 744 550 0 000 005 as well as obtaining strict upper and lower bounds 1 628 1 it grows as l 2 h ere is the growth constant of unconstrained saws in z 2 f orx 1 we provide numerical evidence but no proof that the average walk length grows as l 4 3 another problem we study is that of saws as described above that pass through the central vertex of the square we estimate the proportion of such walks as a fraction of the total and find it to be just below 80 of the total number of saws we also consider hamiltonian walks under the same restriction they are known to grow as l 2 o l2

stratified l ordered quasiuniform limit spaces abstract by making use of the intrinsic lattice valued inclusion orders of l subsets and that of stratified l filters a concept of stratified l ordered quasiuniform limit structure is proposed which is asymmetric and available to establish a framework of asymmetric structures then the category of stratified l ordered quasiuniform limit spaces is introduced and its categorical properties are shown the next objective of the paper is to propose a concept of stratified l ordered principle quasiuniform limit space and we prove that the category of stratified l quasiuniform spaces can be embedded into the category of stratified l quasiuniform limit spaces as a bireflective subcategory moreover two ways of inducing stratified l ordered limit structures from stratified l ordered quasiuniform structures are presented and the method of obtaining stratified 0 1 ordered quasiuniform structures from 0 1 ordered probabilistic quasiuniform limit structures and fuzzy quasi metrics is introduced in the paper

the relationship between various filter notions on agl monoid abstract the notion of a generalised filter is extended to the setting of a gl monoid it is shown that there exists a one to one correspondence between the collection of generalised filters on a set x and the collection of strongly stratified l filters on x specialising to the case where l is the closed unit interval 0 c viewed as a heyting algebra we show that any strongly stratified 0 c filter on x can be uniquely identified with a saturated filter on i x with characteristic value c in this way the notion of a generalised filter unifies various filter notions in particular necessity measures and finitely additive probability measures are specific examples of generalised filters

a comparison of various uniformities in fuzzy topology it is known that the construct fts of stratified fuzzy topological spaces contains non trivial concretely both reflective and coreflective full subconstructs since each of these subconstructs is both initially and finally closed in fts it gives rise to a perfectly viable and autonomous theory of fuzzy topology in this paper this idea is applied to analyze the interrelations between the various notions of uniformity in fuzzy set theory the results show that these notions can be put into a coherent and clear picture if we interpret them as notions of uniformity for certain subconstructs of fts that are concretely both reflective and coreflective or some superconstructs of fuzzy topological spaces

some questions in fuzzy topology the purpose of this paper is to discuss some basic questions related mainly to hutton s l fuzzy unit interval some of those questions are stated here for the first time while some of them are long standing related results are surveyed in some cases

separation axioms and the fuzzy real lines we show that for each lattice l which is completely distributive and equipped with an order reversing involution the canonical topology of the fuzzy real line l is uniformizable in the sense of hutton furthermore this uniformity induces a pseudometric which induces the canonical topology consequently l satisfies the higher order separation axioms of hutton and sarkar more generally we answer most of the open questions concerning l and its subspaces with respect to each of the separation axiom schemes of hutton and sarkar answer some of these same questions for the stratified fuzzy real line c l and its subspaces and analyze c l and its subspaces with respect to the separation axioms of rodabaugh

bicompletion of lowen fuzzy quasi uniform spaces this paper is devoted to the construction of a bicompletion of lowen fuzzy quasi uniform spaces or just 0 1 fuzzy quasi uniform spaces in this paper and the study of that bicompletion which appears to have a number of properties that one could resonably expect in analogy to the situation in ordinary quasi uniform spaces i e denseness of the original spaces in its bicompletion extension property of quasi uniformly continuous maps

phenomenological renormalisation of the self avoiding walk in two dimensions phenomenological renormalisation is used to calculate the exponent v and the connective constant of the self avoiding walk problem on a square lattice a transfer matrix technique is developed for the polymer problem the results indicate that flory s value v 0 75 is true in two dimensions to extremely high accuracy

a common framework for lattice valued uniform spaces and probabilistic uniform limit spaces we study a category of lattice valued uniform convergence spaces where the lattice is enriched by two algebraic operations this general setting allows us to view the category of lattice valued uniform spaces as a reflective subcategory of our category and the category of probabilistic uniform limit spaces as a coreflective subcategory

the general fuzzy filter approach to fuzzy topology ii in this and a subsequent paper by means of an extension of the notion of fuzzy filter a new approach to fuzzy topology is presented whereas this paper is devoted to the general theory of fuzzy filters in part ii this theory is applied on fuzzy topology

lattice valued preuniform convergence spaces using the intrinsic lattice valued inclusion orders of l subsets and of stratified l filters the concept of a stratified l preuniform convergence structure is proposed this convergence structure is asymmetric and can be used to establish a framework of asymmetric lattice valued space structures the category of stratified l preuniform convergence spaces is introduced and some categorical properties are presented a reflective subcategory of stratified l preuniform convergence spaces is found that is categorically isomorphic to strong stratified l convergence spaces originally called stratified l ordered convergence spaces several subcategories of stratified l preuniform convergence spaces are established and relations between the different subcategories are presented we conclude that stratified l preuniform convergence structures introduced here could play a role in the framework of lattice valued asymmetric space structures in lattice valued topology

the urysohn lemma for fuzzy neighbourhood spaces abstract the framework fns of lowen s fuzzy neighbourhood spaces is a special environment for the study of fuzzy topology it encompasses its own metrics uniformities and proximities among other interesting constructions this is a fresh and fast growing field of research it promises to develop quickly to a calculus which combines depth with applicability within this framework we establish the urysohn lemma for the mashhour morsi axiom of n normality the formulation employs the mashhour morsi n euclidean space as the suitable fuzzy analogue of the real line the proof makes use of the artico moresco fuzzy proximities the lowen fuzzy uniformities and the mashhour morsi axiom of n complete regularity

crossover from the dilute to the dense phase for self repelling polymer chains finite size effects and relation to zero component landau ginzburg wilson theory using a recently established perturbative approach we analyse a single polymer chain or a few chains floating in a good solvent contained in a finite box with periodic boundary conditions we calculate to one loop order the partition function and the equation of state relating segment concentration to segment chemical potential and we discuss in detail the chain length distribution for a field theoretic ensemble of chains characterized by fixed our results obey finite size scaling and cover the whole crossover from the dilute to the dense limit where is the critical chemical potential the different limits evolve smoothly from one another the theoretical results for the chain length distribution are compared with monte carlo simulations of self avoiding walks on a cubic lattice we find a good agreement between our results and the simulation data

stratified l m fuzzy quasi uniform spaces in this paper we introduce the notions of stratified l m fuzzy quasi uniform spaces and l m fuzzy quasi uniform bases where l and m are completely distributive lattice and complete residuated lattice respectively we investigate the images and preimages of l m fuzzy uniform base induced by maps we study the relationships between the l m fuzzy quasi uniform space and the stratification of it

on initial and final fuzzy uniform structures part ii this paper is the second part and continuation of a paper for the author published in 2003 and investigating initial fuzzy uniform structures the final fuzzy uniform structures and the final global fuzzy neighborhood structures for the notions of fuzzy uniform structure and of global fuzzy neighborhood structure introduced by the author and others in 1998 in two separate papers are characterized this paper also shows that the expected relations between the final fuzzy uniform structures and the final fuzzy topologies and the final global fuzzy neighborhood structures are indeed true

monoidal closedness of the category of stratified l semiuniform convergence spaces abstract for an integral commutative unital quantale l we show that there exists a tensor product between stratified l semiuniform convergence spaces and with respect to this tensor product that the category of stratified l semiuniform convergence spaces and uniformly continuous maps is a symmetric monoidal category as a result we obtain the monoidal closedness of the category of stratified l semiuniform convergence spaces and uniformly continuous maps

global l neighborhood groups this paper introduces and studies the notion of global l neighborhood group which is defined as a group equipped with a global l neighborhood structure in sense of gahler et al such that both the binary operation and the unary operation of the inverse are continuous with respect to this global l neighborhood structure some examples of global l neighborhood groups are given it is shown that the l topological groups given by ahsanullah in 1984 and later by bayoumi in 2003 are special global l neighborhood groups we also show that all initial and final lifts and hence all initial and final global l neighborhood groups uniquely exist in the category l gnghgrp of global l neighborhood groups these initial and final global l neighborhood groups are defined using the initial and final global l neighborhood structures moreover we show that the l neighborhood groups defined by ahsanullah using the l neighborhood structures in sense of lowen are special global l neighborhood groups for l i is the closed unit interval

on l m fuzzy quasi uniform spaces an l m fuzzy topology is a graded extension of topological spaces handling m valued families of l fuzzy subsets of a referential where l and m are completely distributive lattices when m reduces to the set 2 0 1 a 2 m fuzzy topology is called a fuzzifying topology after ying sostak introduced the notion l m fuzzy uniform spaces the aim of this paper is to study the relationship between 2 m fuzzy quasi uniform spaces and l m fuzzy quasi uniform spaces as well as the relationship between 2 m fuzzy quasi uniform spaces and pointwise l m fuzzy quasi uniform spaces the extension of shi s l quasi uniform space in a kubiak sostak sense it is shown that the category of 2 m fuzzy quasi uniform spaces can be embedded in the category of stratified l m fuzzy quasi uniform spaces as a both reflective and coreflective full subcategory and the former category can also be embedded in the category of pointwise l m fuzzy quasi uniform spaces

the hyperspace of fuzzy sets a natural nontopological fuzzy topological space let x be a uniform topological space then on the family ix resp d x of all nonzero functions resp nonzero uppersemicontinuous functions from x to the unit interval i a fuzzy uniform topology is constructed such that 2x resp 61 x the family of all nonvoid resp nonvoid closed subsets of x equipped with the hausdorff bourbaki structure is isomorphically injected in ix resp i x the main result of this paper is a complete description of convergence in ix by means of a notion of degree of incidence of members of ix immediate consequences are that first it can be shown that this notion of convergence refines some particular useful notions of convergence of fuzzy sets used in applications and that second it follows from its construction and properties that for each ordinary uniform topological space x there exists a natural nontopological fuzzy uniform topology on ix