Fuzzy Separation Axioms and Fuzzy Continuity PDF

Keywords

mathematics, functions, axioms

Abstract

Let (X. T) be a topological space and let W(T) be the set of all lower semicontinuous functions defined from X into the closed unit interval, [0,1]. In this paper we define two fuzzy separation axioms. namely, functionally Hausdorff and complete regularity. Then we prove a) the space (X, T) is functionally Hausdorff if and only if the fuzzy space (X, W(T)) is functionally Hausdorff. and b) the space (X. T) is completely regular if and only if the fuzzy space (X, W(T)) is completely regular.