On F-homotopy and F-fundamental group

Abstract

In general, there are two main ways to define fuzzy topological spaces: (1) given a set X we can take a family of fuzzy subsets of X which satisfies special axioms of topology in X or (2) if τ is a topology at X in the usual sense and A is a fuzzy subset of X, we can consider the special family of fuzzy subsets τ∗ generated by τ in such way that (A, τ∗) is a fuzzy topological space. We present a formalization of the concept of homotopy considering the first point of view of fuzzy topological spaces. We start by maki ng a comparison between the definitions of fuzzy topological spaces in the sense of Morderson [16] and Gunduz [10], as well as their respective concepts of continuity. Furthermore, we investigate issues related to homotopy, function spaces and fundamental group considering this point of view of homotopy.