fuzzy geometry an updated overview abstract this paper briefly reviews work on the fuzzy topology and geometry of image subsets including adjacency separation and connectedness distance and relative position area perimeter and diameter convexity medial axes and thinning as well as some applications of these concepts in image processing and analysis

toeplitz matrix method and nonlinear integral equation of hammerstein type the existence and uniqueness solution of the nonlinear integral equation of hammerstein type with discontinuous kernel are discussed the normality and continuity of the integral operator are proved toeplitz matrix method is used as a numerical method to obtain a nonlinear system of algebraic equations also many important theorems related to the existence and uniqueness of the produced algebraic system are derived finally numerical examples when the kernel takes a logarithmic and carleman forms are discussed and the estimate error in each case is calculated

fuzzy closure spaces abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems but many results can be extended to what are called fuzzy closure spaces or fcs s for short the notions of a subspace a sum and a product are extended to fcs s the hereditary additivity and productivity behaviour of compactness in fcs s is investigated and some weak forms of compactness and fuzzy continuous functions in fcs s are introduced the interaction between fuzzy proximity spaces and fcs s is investigated a necessary background is included for completeness

some additive l fuzzy topological properties abstract the notion of sum for crisp topological spaces have extended to fuzzy topology by ghanim et al 1984 the concept of sum of l fuzzy topological spaces is introduced and its basic properties are discussed by the author 1993 in this paper the additivity of three kinds of l fuzzy topological properties strong separation properties countability and weakly n compactness are studied

on some types of fuzzy connectedness in fuzzy topological spaces abstract in this paper we present some counter examples related to the product of fuzzy connected spaces in addition fuzzy super c5 connectedness is defined and several relations between fuzzy c5 connectedness are obtained finally it is shown that fuzzy c5 connectedness is preserved under some types of continuity

a solution of a nonlinear integral equation in this work we will prove the existence of integrable solution of nonlinear integral equation of type hammerstein volterra of the second kind by using the technique of measure of weak noncompactness and schauder fixed point theorem also the solution of the integral equation is obtained and studied

topological modification of a fuzzy closure space abstract fuzzy topological spaces do not constitute a natural boundary for the validity of theorems and many results can be extended to what are called fuzzy closure spaces fuzzy closure spaces have been introduced in 6 as a generalization of closure spaces 1 in the present paper we introduce the concept of topological modification of a fuzzy closure operator we prove that the topological modification of a fuzzy closure operator u on x is the finest topological fuzzy closure operator on x coarser than u the interaction between the concepts of a subspace and the topological modification of a fuzzy closure operator is also examined

some strong separation in fuzzy topological spaces abstract recently macho stadler et al fuzzy sets and systems 43 1991 95 116 introduced the notion of fuzzy separation using the family of its level topologies lt t t i1 the present work deals with introducing and studying the operations on ri fuzzy topological spaces i 0 1 moreover the notion of fuzzy separation which is well defined as a fuzzy topological concept is described a comparison between the above notions with the analogous fuzzy ones are discussed an acceptable clue which indicates that these notions are equivalent is offered

connectedness on fuzzy topological spaces in this paper properties of connectedness on completely distributive topological lattices definition 2 1 and fuzzy topological spaces 1 are studied some equivalent propositions on the concepts of functions in completely distributive lattices and connected elements in completely distributive lattices and fuzzy topological spaces are proved specially connectedness is characterized both by the r neighborhoods of molecules and c separations for any family li i i i of fuzzy topological spaces the product 1 is connected iff every li i is connected a continuous function maps connected elements onto connected ones the connectedness on the fuzzy real line r l is discussed in the last section as an important example the intervals defined here definition 4 1 must be connected in the fuzzy real line r l and so the intervals defined by rodabaugh in 13 are too any connected element is connected in the fuzzy real line r l if and only if r l r

sums of l fuzzy topological spaces it follows from l ftop being topological over set that there is l fuzzy topological sum in l ftop in this paper we use the final topologies constructed in section 3 of rodabaugh powerset operator foundations of variable basis fuzzy topology in u hohle s e rodabaugh eds mathematics of fuzzy sets logic topology and measure theory the handbooks of fuzzy sets series vol 3 kluwer academic publishers boston dordrecht london 1999 pp 91 116 to characterize l fuzzy topological sum internally and establish connections between l fuzzy topological sum and its factor spaces we create a functor w from l fys the category of l fuzzifying topological space to l ftop and show that w has a right adjoint hence there exists an adjunction from l fys to l ftop moreover w preserves l fuzzy topological sums that already exists in both l fys and l ftop finally we examine certain additivity property of l fuzzy topological spaces these results imply that the topological sum in l ftop a necessary consequence of l ftop being a topological construct is now better understood

extrapolation of nystrom solution for two dimensional nonlinear fredholm integral equations abstract in this paper we analyze the existence of asymptotic error expansion of the nystrom solution for two dimensional nonlinear fredholm integral equations of the second kind we show that the nystrom solution admits an error expansion in powers of the step size h and the step size k for a special choice of the numerical quadrature the leading terms in the error expansion for the nystrom solution contain only even powers of h and k beginning with terms h2p and k2q these expansions are useful for the application of richardson extrapolation and for obtaining sharper error bounds numerical examples show that how richardson extrapolation gives a remarkable increase of precision in addition to faster convergence

connectedness and dimension of gf spaces abstract connectedness of gf spaces defined by means of open closed sets is studied this leads to the notion of a i monotone function using connectedness the notion of a f component is introduced the relationship between connectedness and zero dimensionality is considered

regularly open sets in fuzzy topological spaces abstract this paper is devoted to the study of the role of fuzzy regularly open sets we prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings we prove that under a fuzzy almost continuous and fuzzy almost open map the inverse image of a fuzzy regularly open set is fuzzy regularly open further we define a new type of fuzzy separation axioms fuzzy almost separation axioms it is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology for example in a fuzzy almost t1 space not every fuzzy singleton is closed also a fuzzy space which is fuzzy almost t 2 1 2 as well as fuzzy almost t0 is fuzzy almost regular while in general topology we have to take an almost t2 space in place of almost t0 space

semi induced fuzzy topologies abstract induced fuzzy topologies were first introduced by wong 15 and weiss 14 they were studied by lowen who called them topologically generated fuzzy topologies 7 an induced fuzzy topology includes its modification topology we generalize induced fuzzy topologies to semi induced fuzzy topologies viz those which include their modification topologies the yet more general fuzzy topologies of structure c are also introduced the fully stratified fuzzy topological spaces of structure c are precisely the fuzzy neighbourhood spaces of lowen 4 in subsequent papers this relationship will be established and benefited from the two axioms of semi induction and structure c hold trivially for crisp fuzzy topologies we call such axioms fuzzy structural axioms in fuzzy topology in this paper we analyze the axioms of structure c semi induction and induction in this context we show how these axioms are linked to the three structural asioms of structures a b and d introduced by us in 11 the basic notions and results pertaining to structures a b and d are compiled in the first section the behaviour of warren s fuzzy boundary in semi induced fuzzy topological spaces fts s for short is also explained

on fuzzy almost continuous functions abstract in this paper we redefine the notions of open fuzzy set closed fuzzy set adherent point of a fuzzy set and closure of a fuzzy set all the results pertaining to these notions see velicko 17 are extended to fuzzy setting and several related characterization of fuzzy almost continuous functions are obtained which are the counterparts of the corresponding results in general topological spaces 12 some more properties of fuzzy almost continuous functions are established subsequently a characaterization of normal fuzzy topological spaces is also obtained the notion of fuzzy almost quasi compact mapping is introduced and its characterizations and relationship with fuzzy almost continuous functions are discussed

semi open sets and semi continuity in fuzzy bitopological spaces abstract in this paper the concepts of fuzzy semi open sets and fuzzy semi continuous mappings due to azad 1981 have been generalized to fuzzy bitopological spaces and some of their properties are studied

product integration for volterra integral equations of the second kind with weakly singular kernels we introduce a new numerical approach for solving volterra integral equations of the second kind when the kernel contains a mild singularity we give a convergence result we also present numerical examples which show the performance and efficiency of our method

fuzzy product topologies for x y abstract the aim of this paper is to study the product topologies in fuzzy topology the notion and main properties of fk spaces which play an important role in the sequel are introduced sufficient conditions for which the product of fuzzy identification maps is a fuzzy identification map are given

extrapolation method of iterated collocation solution for two dimensional nonlinear volterra integral equations in this paper we study the numerical solution of two dimensional nonlinear volterra integral equation by collocation and iterated collocation method asymptotic error expansion of iterated collocation solution is obtained using richardson s extrapolation we show that the accuracy of numerical solution in the iterated collocation method can be improved greatly some numerical examples are given to illustrate this theory

the connectedness in lowen spaces abstract a new f connectedness notion is introduced and its relation with the other connectedness notions are demonstrated furthermore the properties of f sets and f connectedness in lowen spaces are also investigated

on zero dimensionality in fuzzy topological spaces abstract different concepts of zero dimensionality in fuzzy topological spaces are studied it is shown that the c zero dimensionality and the strongly c zero dimensionality are not good extensions in the lowen sense of the zero dimension for the inductive topological dimensions ind and ind respectively some properties of these spaces and their relationship with the adnadjevic fuzzy topological dimension are also stated

on smooth topological spaces ii separation axioms in the present paper we introduce the notions of smooth separation axioms in several ways and investigate some of their properties and the relations between them in the general framework of smooth topological spaces

convergence analysis of hybrid functions method for two dimensional nonlinear volterra fredholm integral equations abstract an interesting and computationally efficient scheme is proposed for solving a class of two dimensional nonlinear volterra fredholm integral equations the collocation method in conjunction with two dimensional hybrid functions is utilized to convert these types of equations to a nonlinear system of equations that can be solved numerically by the newton s method the major advantages of this method are simplicity of performing and favorable convergence rate for an approximate solution the convergence analysis of the hybrid functions and the error bound of the presented method are discussed in detail moreover some numerical experiments are provided to confirm our theoretical analysis

on the sum of l fuzzy topological spaces abstract h ghanim et al separation axioms subspaces and sums in fuzzy topology j math anal appl 102 1984 189 202 have extended the notion of sum for crisp topological spaces to fuzzy topological spaces and discussed the additivity for some fuzzy topological properties in this paper the concept of the sum of l fuzzy topological spaces is presented and its basic properties is discussed as the main results of the paper the additivity of separability and compactness in l fuzzy topological spaces is studied

fuzzy connected sets in fuzzy topological spaces abstract the interrelationship between different notions of connectedness of fuzzy sets introduced by ming and ming zheng chong you saha and ajmal and kohli is investigated a new concept of connectedness called c 5 connectedness of a fuzzy set is introduced and the validity of the standard results for this new concept of connectedness is examined

fuzzy alpha sets and alpha continuous maps abstract in this paper we generalize the notion of sets to fuzzy spaces we also introduce the concepts of fuzzy continuous and fuzzy open mappings and discuss their relations with fuzzy continuous and other weaker forms of fuzzy continuous mappings counterexamples are given to show the non coincidence of these mappings

discrete sets in fuzzy topological spaces abstract we introduce the notion of discrete set in fuzzy topological spaces and prove that a fuzzy hausdorif topological space x has an infinite discrete set if the set x is infinite

fuzzy preopen sets and fuzzy preseparation axioms abstract in this paper the concept of preopen sets due to a s mashhour m e abd el monsef and s n el debb 7 has been generalised to the fuzzy setting further fuzzy separation axioms have been introduced and investigated with the help of fuzzy preopen sets

on a method for solving an integral equation in the displacement contact problem in this paper the solution in a series form of the integral equation of the mixed type in the space l w xc 0 t is obtained where w x y z

on solution of nonlinear abel volterra integral equation abstract this paper is devoted to studying the nonlinear abel volterra integral equation of the form m x a x x 0 t x t 1 dt f x 0 x d with 0 andm r m 0 1 2 the uniqueness of the solution is proved and the asymptotic behavior of x asx 0 is obtained provided thata x andf x have special power asymptotics near zero the solution x in closed form is given in some cases

fuzzy separation axioms and fuzzy continuity in fuzzy bitopological spaces abstract let x 1 2 be a bitopological space and i i 1 2 be the set of all lower semi continuous functions defined from x into the closed unit interval 0 1 in this paper we have succeeded in showing goodness of extension of separation axioms for fuzzy bitopological spaces namely we prove the space x 1 2 is p t i p t iw p regular and p normal iff the fuzzy bitopological space x 1 2 is p t i p t iw p regular and p normal

growth of weil petersson volumes and random hyperbolic surfaces of large genus in this paper we investigate the geometric properties of random hyperbolic surfaces of large genus we describe the relationship between the behavior of lengths of simple closed geodesics on a hyperbolic surface and properties of the moduli space of such surfaces first we study the asymptotic behavior of weil petersson volume vg n of the moduli spaces of hyperbolic surfaces of genus g with n punctures as g then we discuss basic geometric properties of a random hyperbolic surface of genus g with respect to the weil petersson measure as g

fuzzy topologies and topological space objects in a topos abstract the purpose of this paper is to point out the link between lowen s fuzzy topologies and topological space objects in the topos l set as the main result we obtain the following theorem lowen s fuzzy topologies are the external version of the internal topologies in l set

locale theory and fuzzy topology abstract for a lattice l which is a spatial frame it is shown that every l fuzzy topology t on a set x is isomorphic as a frame to a topology on the set x pt l where pt l is the set of points of l when t is topological the topology on x pt l is the product topology thus providing a simple test of goodness

the numerical solution of nonlinear two dimensional volterra fredholm integral equations of the second kind based on the radial basis functions approximation with error analysis in this paper we present a numerical method for solving two dimensional nonlinear volterra fredholm integral equations of the second kind the method approximates the solution by the discrete collocation method based on radial basis functions rbfs constructed on a set of disordered data the proposed method is meshless since it does not require any background mesh or domain elements error analysis of this method is also investigated numerical examples which compare the proposed method with 2d tfs method 4 approve its supremacy in terms of accuracy and computational cost using various rbfs we have concluded that mq rbf is the best choice for the proposed method

separation axioms for fuzzy spaces abstract using the concepts of fuzzy points as introduced by wong 15 and of belonging to as introduced by r srivastava s n lal and a k srivastava 13 we introduce several notions of fuzzy separation axioms and examine their productivity relations between these axioms have been observed we also introduce four types of separated fuzzy sets and clarify some relations between them

a fuzzy topology associated with a fuzzy finite state machine abstract given a fuzzy finite state machine m q a fuzzy closure operator is defined which induces a lowen type fuzzy topology in q the concepts of separation of fuzzy subsystems and connectedness of fuzzy finite state machines are developed some results on connectedness and weak connectedness of fuzzy subsystems are obtained characterizations of these concepts in terms of the fuzzy topology are also obtained

connectedness in fuzzy topological spaces abstract we introduce four notions of connectedness for an arbitrary fuzzy set and discuss all the implications that exist between them using these notions various equivalence relations are defined on the set of fuzzy points components and quasi components are formed as the union of certain equivalence classes a fuzzy space is shown to be a dispoint union of its components in all the four cases and non overlapping union of its quasi components

on some fuzzy connectedness concepts abstract in this paper we examine whether or not the concepts of fuzzy strong connectedness fuzzy super connectedness and fuzzy c connectedness can be viewed as e connectedness in the category fts of fuzzy topological spaces in the sense of preuss

various fuzzy topological notions and fuzzy almost continuity abstract we extend the notion of almost continuity in the sense of husain 1966 to the fuzzy setting we obtain a pointwise characterization of the notion by dual point and fuzzy net also we formulate conditions under which the two notions of fuzzy almost continuity the one defined in this paper and the one defined by ajmal and azad 1990 turn out to be equivalent the main idea behind this work is to show that using the localized approach developed in earlier papers the study of fuzzy almost continuity can be carried out as successfully as that of its counterpart in general topology in the process we exhibit the compatibility of various existing fuzzy topological notions such as fuzzy regularity c i connectedness i 3 4 c i local connectedness i 3 4 fuzzy t 1 axiom fuzzy t 2 axiom etc

on fuzzy d continuity and a near compactness in fuzzy topological spaces abstract the concept of fuzzy continuity was introduced by saha 18 mashhour et al have introduced the concept of near compactness in fuzzy setting in this paper we give a characterization of fuzzy continuity and fuzzy nearly compactness also we investigate the image of fuzzy nearly compact spaces under some types of functions finally a refinement is made to some results in 15 17

a new approach to fuzzy topological spaces and fuzzy perfect mappings abstract a net theoretic approach is provided for defining a fuzzy topological space fuzzy topological spaces so defined form a category the main features and advantages of this category which is denoted by n here are discussed the notion of a perfect mapping is introduced and studied in the fuzzy setting it is found that in n a fts is n compact iff any mapping x x where x is any singleton is fuzzy perfect a fuzzy continuous mapping x y from an n compact fts x to a hausdorff fts y is fuzzy perfect in n however these results do not hold in c the chang s category in general it is found that the divergences in the study of fuzzy perfect mappings disappear if the study is carried out in n instead of c

on a method for solving a two dimensional nonlinear integral equation of the second kind in this article the existence of at least one solution of a nonlinear integral equation of the second kind is proved the degenerate method is used to obtain a nonlinear algebraic system where the existence of at least one solution of this system is discussed finally computational results with error estimates are obtained using maple software

fuzzy topology fuzzy closure operator fuzzy compactness and fuzzy connectedness abstract in this paper definitions of fuzzy closure operator fuzzy compactness and fuzzy connectedness are given in a redefined fuzzy topological space and then some characteristic properties of fuzzy closure operator product theorems of fuzzy compactness invariance of fuzzy compactness and fuzzy connectedness under gradation preserving maps and invariance of fuzzy connectedness under the fuzzy closure operator are studied

an explicit upper bound for weil petersson volumes of the moduli spaces of punctured riemann surfaces an explicit upper bound for the weil petersson volumes of punctured riemann surfaces is obtained using penner s combinatorial integration scheme from 4 it is shown that for a fixed number of punctures n and for genus g increasing

a note on some ft 2 concepts abstract in this note we study in particular the fuzzy hausdorffness concepts introduced by adnadjevic 1 ganguly and saha 4 and sarkar 17

t product fuzzy topology abstract using the notion of a t norm the t product fuzzy topological space of two fuzzy topological spaces is defined the validity of some standard results on product fuzzy topology defined by wong 10 is examined in the case of t product fuzzy topology

fuzzy topological properties and hereditariness some known compactness notions and separation axioms already given in chang fuzzy topological spaces are extended to a more general context of categories where i topological spaces on arbitrary i sets are defined the invariance under morphisms in these categories and the usual hereditary conditions of the considered topological properties in such a context are investigated

connectedness in l fuzzy topological spaces based on the consideration to the layer structures of fuzzy lattices and the level topologies of l fuzzy topological spaces a connectedness is defined for an arbitrary l fuzzy set in this paper this definition reflects the degree of connectivity of an l fuzzy set it is shown that the connectedness of l fuzzy topological spaces is an l good extension multiplicative and preserved under continuous l valued zadeh functions and that the inverse limit of continuums is a continuum general l fuzzy intervals and h intervals are defined and connectedness of them are proved it is also shown that the connectedness of an l fuzzy topological space is equivalent to the connectedness of its induced i l fuzzy topological space

overlapping families and covering dimension in fuzzy topological spaces abstract a non classical approach is used to introduce notions of overlapping families of fuzzy sets and the order of a family of fuzzy sets leading to a coherent theory of covering dimension in fuzzy topological spaces class of semicrisp fuzzy topological spaces is introduced which provides a suitable framework for the study of dimension function in the fuzzy setting

epimorphisms in categories of separated fuzzy topological spaces abstract the categorical theory of closure operators is used to characterize the epimorphisms in certain categories of separated fuzzy topological spaces in the sense of lowen these include the 0 t 0 spaces of wuyts and lowen the ft s spaces of ghanim kerre and mashhour and the t 2 spaces of rodabaugh

a comparison of some ft 2 concepts abstract recently ghanim kerre and mashhour 2 have introduced and examined a fuzzy hausdorffness concept in this paper we compare it with some of the other existing concepts of fuzzy hausdorffness and note thereby that though it is a good extension of hausdorffness it is independent of several other fuzzy hausdorffness concepts currently in use

low cost numerical solution for three dimensional linear and nonlinear integral equations via three dimensional jacobi polynomials in recent years numerical methods have been introduced to solve two dimensional volterra and fredholm integral equations in this study a numerical scheme is constructed to solve classes of linear and nonlinear three dimensional integral equations volterra fredholm and mixed volterrafredholm this operational approach is proposed to easily and directly solve these equations at low computational costs the scheme is based on the jacobi polynomials on the interval 0 1 where three variable jacobi polynomials are introduced and their operational matrices of integration and product are derived compared to other existing methods for multidimensional problems the jacobi operational method eliminates the time consuming computations and solely employs the one dimensional operational matrix to construct corresponding multidimensional operational matrices the absolute error of the proposed method is almost constant on the studied interval even at higher dimensions confirming the stability of the proposed operational jacobi method required theorems on the convergence of the method are proved in jacobi weighted sobolev space it is established that the error function vanishes as n increases the method is evaluated using several illustrative examples which indicate the proposed method with lesser computational size compared to the blockpulse functions differential transform and degenerate kernel methods

zero dimensional and strongly zero dimensional fuzzy topological spaces abstract concepts of zero dimensionality strong zero dimensionality and total disconnectedness are extended to fuzzy topological spaces their basic properties and interrelationships among them are studied a sum theorem for strongly zero dimensional fuzzy topological spaces is also obtained

category n and functions with closed fuzzy graph abstract a net theoretic approach for defining a fuzzy topological space is provided the fuzzy topological spaces so obtained form a category which we denote by n in this paper it is found that the limitations exhibited by the chang category particularly with respect to projections closure of a fuzzy set compactness etc no longer exist in n the notion of closed fuzzy graph is investigated the divergences shown by this notion are immediately put to rest if the study is carried out in n instead of c the chang category

new approach to solve two dimensional fredholm integral equations abstract in this paper we present an efficient iterative method based on quadrature formula to solve two dimensional nonlinear fredholm integral equations we investigate the convergence analysis of the proposed method the error estimation is given in terms of uniform and partial modulus of continuity in addition we show the numerical stability analysis of the method with respect to the choice of the first iteration finally some numerical experiments confirm the theoretical results and illustrate the accuracy of the method

on lower separation axioms abstract in 3 mashhour et al introduced the concept of fuzzy disjointness two fuzzy sets a b in x are said to be fuzzy disjoint if a co b where co b is the complement of b using this concept they introduced fti separation axioms as a generalization for the basic separation axioms ti i 1 4 in 5 singal and rajvanshi used the concepts of regular open fuzzy sets 1 and fuzzy disjointness to introduce some fuzzy almost separation axioms which are stronger than those of mashhour unfortunately some results in 5 are incorrect in this paper we use the concept of the quasi coincident relation 4 to restate lower fuzzy separation axioms and give a corrected version for some definitions and results in 5

fuzzy t neighbourhood spaces part 3 t separation axioms we address the problem of identifying a useful set of mutually compatible separation axioms for each category t fns of t neighbourhood spaces it should contain one of t complete regularity that characterizes t uniformizability as indeed we achieve here this seems to necessitate the parameterization of most separation axioms by the triangular norm t with the exception of the two axioms t0 and r0 which have categorical definitions valid in any topological category we introduce t separation axioms in terms of t and fuzzy closure operators only making them meaningful for the whole of fts we then characterize them within t fns in terms of t fuzzy closures of crisp fuzzy subsets and t neighbourhoods we study our t axioms and establish some entailments between them our t complete regularity commits us to investigate a t real line which is a t neighbourhood space induced by a certain probabilistic t metric due to hohle fuzzy sets and systems 1 1978 311

a family of methods for abel integral equations of the second kind abstract a class of methods depending on some parameters are introduced for the numerical solution of the abel integral equations of the second kind some bounds on the parameters are determined so that the corresponding methods have infinite stability intervals

basic notions for fuzzy topology 1 abstract a new notion of fuzzy real line is presented applications are obtained when solving the problem of generating fuzzy topologies by fuzzy metrics the results provide a fundamental example as a basis for a convergence based approach to fuzzy topology

fuzzy connectedness in intuitionistic fuzzy topological spaces the aim of this paper is to introduce several types of fuzzy connectedness in intuitionistic fuzzy topological spaces defined by coker 1997 this construction is based on the idea of intuitionistic fuzzy set developed by atanassov 1983 1986 atanassov and stoeva 1983 we also investigate some interrelations between these types of fuzzy connectedness together with the preservation properties under fuzzy continuous functions

connectedness and local connectedness in fuzzy topological spaces and heyting algebra valued sets abstract in this paper we introduce four notions of local connectedness in fuzzy topological spaces the question of these notions to be good extensions is discussed and their preservation under fuzzy quotients fuzzy sums and fuzzy products is investigated moreover we introduce the notion of quasi local connectedness which is a peculiarity of the fuzzy setting

a meshless method for solving nonlinear two dimensional integral equations of the second kind on non rectangular domains using radial basis functions with error analysis in this paper we present a numerical method for solving two dimensional nonlinear fredholm integral equations of the second kind on a non rectangular domain the method utilizes radial basis functions rbfs constructed on scattered points as a basis in the discrete collocation method the proposed scheme is meshless since it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional nonlinear integral equation to the solution of a nonlinear system of algebraic equations error analysis is presented for this method finally numerical examples are included to show the validity and efficiency of the new technique

l topological spaces as spaces of points the main background of this paper is a functor from the category of l topological spaces to the category of topological spaces which is defined by means of an attachment a notion recently introduced in the lattice l and has very nice properties under the assumption of spatiality the pu liu s quasi coincidence relation largely used to study 0 1 topological spaces is determined by a suitable attachment in 0 1 so the results described here apply to that situation this functor allows to import topological concepts into the fuzzy setting directly from the classical context meanwhile this provides an evaluation of the relevance and of the consistency of basic notions in fuzzy topology as well as a critical view on how these have been introduced and treated up to now an overview of the relationship between spatial attachments and textures is outlined in the last part of the paper