On Some Hereditary Coreflective Subcategories in Fuzzy Topology

Abstract

We first show that if A is a coreflective subcategory of the category FTS of fuzzy topological spaces, then the subcategory of FTS consisting of all the subspaces of spaces of objects of A, is a hereditary coreflective subcategory of FTS. As the category of all those fuzzy topological spaces, which can be written as a disjoint union of indiscrete or discrete fuzzy topological spaces, is coreflective, we show that it is also hereditary coreflective. We show that the category of all those fuzzy topological spaces, in which each open set is closed and the category of all those fuzzy topological spaces, which are closed under arbitrary meets, are hereditary coreflective subcategories of the category of fuzzy topological spaces.