ON THE TOPOLOGY GENERATED BY SEMI-REGULAR SETS

Abstract

In this paper we study compactness properties of spaces whose topologies are generated by the family of semi-open sets or the family of semi-regular sets of a given topological space (X, tau). In addition, we obtain characterizations of extremally disconnected spaces and show that the concepts of semi-compactness and semi-countable compactness coincide. We also prove that the family of semi-regular sets of a space constitutes a topology iff the corresponding semi-regularization space is locally indiscrete.