More on Fuzzy Topological Spaces on Fuzzy Space

TL;DR

This paper extends the theory of fuzzy topological spaces by introducing new definitions, theorems, and various types of fuzzy topologies, along with studying boundary points and separation axioms on fuzzy spaces.

Contribution

It provides new definitions, theorems, and types of fuzzy topological spaces, filling gaps in previous work and exploring boundary, exterior, isolated points, and separation axioms.

Findings

Introduction of co-finite and co-countable fuzzy topologies

Analysis of boundary, exterior, and isolated points in fuzzy spaces

Study of separation axioms on fuzzy spaces

Abstract

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of fuzzy spaces. Dip's approach helps to rectify the deviation in some definitions of fuzzy subsets in fuzzy topological spaces. In this paper, further definitions, and theorems on fuzzy topological space fill the lack in Dip's article. Different types of fuzzy topological space on fuzzy space are presented such as co-finite, co-countable, right and left ray, and usual fuzzy topology. Furthermore, boundary, exterior, and isolated points of fuzzy sets are investigated and illustrated based on fuzzy spaces. Finally, separation axioms are studied on fuzzy spaces.