Higher separation axioms in L-topologically generated (L)-topological spaces
The main result of this paper is a theorem about inserting a pair of semicontinuous L-real-valued functions which extends the insertion theorem of Kubiak [Comment. Math. Univ. Carolinae 34 (1993) 357-362] from L = {0, 1}to an arbitrary meet-continuous lattice L (endowed with an order-reversing involution). With this result it is shown that the normality-type separation axioms in TOP(L) are preserved by the functor which takes an L-topological space X to the (sic)(L)-topological space Omega(L)(X) obtained by providing the set X with the (sic)(L)-topology consisting of all lower semicontinuous functions from X to (sic)(L). The same is proved for the case of the regularity axiom. (C) 2001 Elsevier Science B.V. All rights reserved.
l-topologically generated (l)-topological spaces insertion regularity semicontinuous l-real functions normality axioms l-topological modification of an (l)-topological space