Mixed Fuzzy topological space its Hausdorff properties and base

Abstract

In this article, mixed fuzzy topology and its topological properties have been studied. Mixed fuzzy topology is defined with the help of quasi-coincidence and closure of a fuzzy set in one of the fuzzy topologies. Thus, a new fuzzy topology is generated from the given two fuzzy topologies. This new fuzzy topology may or may not contain the topological properties of the parent topologies. This study identifies some topological properties that are carried to the mixed fuzzy topology from the given parent fuzzy topologies and some other properties which are not carried to the mixed fuzzy topology. Here a base for mixed fuzzy topology from the bases of the given parent topologies is constructed. Considering the regularity of one of the parent topologies mixed fuzzy topology is investigated. Hausdorff’s properties of mixed fuzzy topological spaces are also discussed. It is now of general interest to know which properties are carried to the mixed topology and which are not. A few of these are being tried to answer here in this paper.