Wallman t 1 -compactifications as epireflections

Abstract

The purpose of this paper is to generalize the recent results of Harris concerning the functorial properties of the Wallman compactification of a T 1 -space. Steiner has introduced the Wallman-type compactifications of T 1 -spaces endowed with separating bases. We introduce a definition of morphism between such spaces to obtain a category which we denote by wosep. We prove that the Wallman-type compactification on objects can be extended to a functor on wosep and that the compact objects give an epireflective subcategory of wosep.