On obtaining an ε - Compactification of a topological space

Abstract

It is known that one of the most elementary and functional notions of finiteness in analysis, algebra and topology is the notion of compactness yet mathematicians work with many non-compact topological spaces, which have applications that require some properties of compact spaces. The purpose of this paper is to check the conditions under which if Z is a compactification of W, under what condition can a continuous real-valued function defined on W be extended continuously to Z where Z is an ε - compactification of W.