Separation Axioms, Subspaces and Product Spaces in Fuzzy Topology PDF

Keywords

fuzzy topology, subspaces, separation axioms

Abstract

Let (X, τ) be a topological space and let ω(τ) be the set of all lower semi-continuous functions defined from X into the closed unit interval [0,1]. We prove the following result in this paper: If {(Xi, τi): i⋲ I} is a collection of topological spaces, then ω(I| τ1)= I|ω(τ1). We introduce some fuzzy separation axioms and the we study their hereditary and productive properties. We also study the relation between spaces having the fixed point property and fuzzy connected spaces.