On the relationship between several basic categories in fuzzy topology

Abstract

In this paper, a process, which associates with every fibre-small topological
category A and every completely
distributive lattice L another
topological category called the co-tower extension of A, is introduced to investigate the relationship between several
basic categories in fuzzy topology. It is proved that the category of
stratified Šostak L-fuzzy topological spaces is the co-tower
extension of the category of stratified Chang-Goguen
spaces; and the category of L-fuzzifying topological
spaces (which is isomorphic the category of fuzzy neighborhood spaces when L=
[0,1]) is the co-tower extension of the category of topological spaces. Thus,
in some sense, we can say that properties of the
category of stratified Šostak L-fuzzy topological spaces and L-fuzzifying
topological spaces are determined by the categories of stratified Chang-Goguen
spaces,
topological spaces and the lattice L. Therefore it
can be said that in fuzzy topology the category of (stratified) Chang-Goguen
topological spaces is more basic and more important
than the other categories.

Mathematics Subject
Classification (2000):
54A40, 54B30



Quaestiones Mathematicae 25 (2002), 289-301