THE SUBSPACE PROBLEM IN THE TRADITIONAL POINT-SET CONTEXT OF FUZZY TOPOLOGY

Abstract

We consider old and new categories of fuzzy topological spaces where objects associated to arbitrary fuzzy sets are considered and fuzzy topological subspaces are characterized as particular subobjects. Also fuzzy homeomorphisms are characterized in the considered categories. We unify notation and language and compare the different frameworks in the traditional point-set context. We use only the real unit interval as a lattice in order to define fuzzy sets.