r-WEAK cb SPACES

Abstract

The purpose of the paper is to introduce the notion of r-weak cb spaces as ageneralization of weak cb spaces. The r-weak property of a space is defined with the help of a stronger form of normal upper semi continuous functions viz. strongly normal upper semi continuous (s-nusc) function.  A stronger form of regular closed subsets called strongly regular (s-regular) closed subsets turns out
to be the natural tool for defining the new function.  The r-weak cb spaces arecharacterized by a increasing cover of s-regular open (i.e. complement of s-regular closed) subsets and a decreasing sequence of s-regular closed subsets.  Some of the properties of the newly introduced spaces and its interrelationship with other spaces are investigated.