\(\lambda _{c}\)-Open Sets and \(\lambda _{c}\)-Separation Axioms in Topological Spaces

Abstract

The aim of this paper is to introduce a new class of sets called \({{\lambda }_{c}}\)-open sets and to investigate some of their relationships and properties. Further, by using this set, the notion of \({{\lambda }_{c}}\)-\({T}_{i}}\) spaces ( \(i = 0,1/2, 1, 2\)) and \({{\lambda }_{c}}\)-\({{R}_{j}}\) spaces ( \(j = 0, 1\) ) are introduced and some of their properties are investigated.