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.
Amos Otieno Wanjara (Thu,) studied this question.