Almost $\beta$-Regular Spaces and Almost $rg\beta$-Closed Functions

Abstract

The aim of this paper is to introduce and study a new class of spaces, namely almost $\beta$-regular spaces which are generalizations of the concepts of almost regular spaces and $\beta$-regular spaces and to obtain some characterizations of almost $\beta$-regular spaces. Further, by using $rg\beta$-closed sets, we define almost $rg\beta$-closed functions and to obtain preservation theorems of almost $\beta$-regular spaces. The relationships among p-regular, $\beta$-regular, almost regular, almost p-regular, almost $\beta$-regular spaces are investigated. The main result of this paper is that almost $\beta$-regularity is preserved under M-$\beta$-open $\beta$-$rg\beta$-closed surjective R-maps.