On Sw*- Regular Spaces

Abstract

The purpose of this paper is to present and investigate a new class of topological spaces known as S_w*-regular spaces, by utilizing the concept of Sw-regular sets and some of its properties. which is introduced in 2009 by L. S. Abddullah and A. B. Khalaf [1], the new class is properly contained in S^*- regular space [2], [3], means that S_w*- regular spaces is a stronger form to the space S^*- regular. Several characterizations, properties and relationships of S_w*- regular space with other spaces such as, Sw-compact, extremally disconnected, regular, semi-regular, Sw-T₂ and Urysohn spaces has been studied. Furthermore, several properties of S_w*- regular spaces with some functions such as, continuous, strongly continuous, open, clopen and Somewhat open functions are also explored. In addition we investigate that S_w^*- regular space has a topological property, while it has not a hereditary property, only by adding certain conditions such as, a subspace is open or, if the subspace of an S_w^*-regular submaximal space is  preopen, then it becomes an S_w*- regular.