Some categorical aspects of fuzzy topology

Research in recent years has revealed that the construct of fuzzy topologic al spaces behaves quite differently from that of topological spaces with re spect to certain categorical properties. In this paper we discuss some of t hese aspects. Since the topological construct L-FTS contains nontrivial bot h initially and finally closed full subconstructs, and each such construct gives rise to a natural autonomous theory of fuzzy topology, it can be said to some extent that fuzzy topology should consist of a system of closely r elated topology theories, including the classical topology theory as a spec ial case, with each applying to one such subconstruct. Therefore in the fir st part of this paper the theory of sobriety is established for each finall y and initially closed full subconstruct of L-FTS to illustrate this idea. The second topic of this paper is the relationship between the construct of stratified L-fuzzy topological spaces and several other familiar construct s in fuzzy topology, for example, the constructs of Sostak fuzzy topologica l spaces and L-fuzzifying topological spaces. (C) 2000 Academic Press.