Gamma-Regular-Open Sets and Gamma-Extremally Disconnected Spaces

Abstract

The aim of this paper is to introduce a new class of sets called Gamma-regular-open sets in topological spaces (X, t) with an operation Gamma on t together with its complement which is Gamma-regular-closed. Also to define a new space called Gamma-extremally disconnected, and to obtain several characterizations of Gamma-extremally disconnected spaces by utilizing Gamma-regular-open sets and Gamma-regular-closed sets. Further Gamma-locally indiscrete and g-hyperconnected spaces have been defined.