A study of ?-Connectedness and Strongly ?-Connectedness in Topological spaces and Their Applications

Abstract

This paper is devoted to introduce and study new concept of separated sets called, ?-separated sets by utilizing another generalized open set namely, ?-open, as well with this concept we introduce a new class of connected spaces which is called strongly ?-connected spaces and investigate some basic properties of ?-connected spaces. Several characterizations and fundamental properties concerning of such classes of connected spaces with some ? -Separation axioms and compact spaces are obtained. The behavior of ?-connected spaces with respect to several types of well-known mappings is discussed. Furthermore, we construct new topological spaces on a connected graph.