January 2020, Vol. 3, Issue 1, p. 1-4.​​

On obtaining an ε - Compactification of a topological space
Amos Otieno Wanjara
School of Mathematics, Statistics and Actuarial Science, Kaimosi Friends University College, P.O BOX 385-50309, Kaimosi-Kenya.
*Corresponding author’s e-mail:


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.

Keywords: Compactification; Equivalent Compactification; the one point Compactificaton; Hausdorff space.


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