Some topological properties of e-space and description of τ-closed sets

Abstract

In this paper we study preserving properties of e-space under the normal functors Π^n, SP^n and exp_n. We prove that when a topological space X is an e-space, the spaces X^n, SP^nX and exp_nX are also e-spaces. We also study the behavior of e-continuity in mappings, proving that the functors Π^n, SP^n and exp_n
preserve the e-continuity. In addition, we introduce the notions of τ-boundary points, τ-cluster points and τ-boundary of a set and study many of their properties.