The fundamental group of soft topological spaces

Abstract

In this paper, we introduce the notion of fundamental group for soft topological spaces. To do so, we define soft paths, soft loops and the notion of \(\xi \)-soft path homotopy, and study some of their basic properties. We also show that the fundamental group of an \(\varepsilon \)-soft topological group is commutative. Finally, we define the category soft topological of spaces and prove that \(\pi _1^\mathrm{soft}\) is a functor from this category to the category of groups.