On Sw*- Regular Spaces

Abstract

The purpose of this paper is to present and investigate a new class of topological spaces known as Sw*-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 Sw*- regular spaces is a stronger form to the space S*- regular. Several characterizations, properties and relationships of Sw*- 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 Sw*- regular spaces with some functions such as, continuous, strongly continuous, open, clopen and Somewhat open functions are also explored. In addition we investigate that Sw*- 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 Sw*-regular submaximal space is preopen, then it becomes an Sw*- regular.