On SW*- regular spaces

Abstract EN

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