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

Abstract

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