Fundamental Group of Rough Topological Spaces

Abstract

In this paper we study and define the concept of the fundamental group of rough topological spaces (RTSs), which deeply depends on the concepts of rough sets (RSs) and rough topology (RT). Working towards this stated objective, we define the concept of rough path (RPt) which gives room for the introduction of rough loop (RL). We also define the concepts of rough homotopy (RH) and later shows that it is indeed an equivalence relation. We introduce the fundamental group of rough topological spaces by showing that all the group axioms satisfied. Also, this paper establish the fact that most of the results in fundamental group of ordinary topological spaces are also hold for the fundamental group of rough topological spaces.