On Beta;-sets in betaB3;-spaces

Abstract

We consider a collection of subsets of a set X defined in terms of a function on ℘(X), called the γ−open sets, which is not a topology but we show that some of the results established for topologies are valid for this collection. In particular, we define δγ−open sets in a γ−space and characterize its properties. Also, we discuss the properties of γ−rare sets and characterize δ γ −open sets in terms of γ−rare sets.