Certain Spaces and Functions by Using Еc and δ-ßc-Open Sets

Abstract

The concepts of continuity of functions, compactness and separation axioms are a significant and basic topics not only for the theory of classical point set topology but also of other advanced branches of mathematics, of course their weak and strong forms are important too. Semi-open sets, α-open sets, pre-open sets, semi-pre-open sets, b-open sets, δ-pre-open sets, e*-open sets, e-open sets, Еc -open sets and δ-ßc-open sets play an important role in generalization of continuity, compactness and separation axioms. Many authors introduced and investigated various types of modifications of generalization of continuity, compactness and separation axioms by using these generalized open sets and great number of papers dealing with such concepts has been appeared. Moreover, generalized open sets play a very important role in general topology and they are the research topics of many topologists worldwide. In our thesis we introduce and investigate new classes of generalized open sets called Еc-open and δ-ßc-open sets and by utilizing these types of generalized open sets we introduce new concepts of generalized continuous functions in a topological space, namely, Еc-continuous and δ-ßc-continuous functions. Moreover, we offer and study new classes of spaces called, Еc and δ-ßc-compact spaces via Еc and δ-ßc- open sets, as well as we present new types of separation axioms in topological spaces namely Еc and δ-ßc-separation axioms via Еc and δ-ßc-open sets, and in the context of these generalized open sets we study the Еc and δ-ßc-Regulare spaces and the Еc and δ-ßc-Normal spaces.