Operation on Regular Spaces

Abstract

In this paper, we introduce the concept of \(R_{\gamma}\)-open sets as a strong of \(\gamma\)-open sets in a topological space \((X,\tau)\). Using this set, we introduce \(R_{\gamma}\)-\(T_0\), \(R_{\gamma}\)-\(T_{\frac{1}{2}}\), \(R_{\gamma}\)-\(T_1\), \(R_{\gamma}\)-\(T_2\), \(R_{\gamma}\)-\(T_3\), \(R_{\gamma}\)-\(T_4\), \(R_{\gamma}\)-\(D_0\), \(R_{\gamma}\)-\(D_1\) and \(R_{\gamma}\)-\(D_2\) spaces and study some of its properties. Finally we introduce \(R_{(\gamma,{\gamma^{'}})}\)-continuous mappings and give some properties of such mappings.