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: firstname.lastname@example.org
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.
- Ennis R, Jorge V. Operator Compactification of Topological spaces. Divulgaciones Matematicas 2000;8:163-7.
- Max FP. Topological Reconstruction and Compactification Theory, University of Oxford, Trinity, 2015.
- Tarizadeh A, Rezaee Huri MR. On the Compactification of Spaces with Applications, Math Ac 2019.
- James D. Topology, (Allyn and Bacon series in Advanced Mathematics) Allyn and Bacon, Inc, Boston, 1966.
- Munkress, James R. Topology (2nd ed.) New York, Prentice Hall, 2008.
- Laugwitz. On Compactification using the intuitively infinite and non- compact topological space , 2008.
- Keesling J. The Stone-Cech Compactification and shape dimension. Topology Proceedings 1977;2:483-508.
- Kelly J, Namioka L. I. Linear Topological spaces, Springer-Verlag, 1982.
- Kelly JL. General topology, Springer-Verlag, 1991.
- Murray F. Linear transformations in LP, P>1. Trans Amer Math Soc 1936;39:83-100.
- Narici L, Bakestein E. Topological vector spaces, Marcel Dekker, New York, 1985.
- Stone MH. Applications of the theory of Boolean Rings to General topology. American Mathematical Society 41(1937;41:375-481.
- Wiener N. Limit in terms of continuous transformation. Bull Soc Math Fr 1933; 50:119-34.
- Walker RC. The Stone-Cechcompactification. Berlin, Springer-Verlag, 1974.
- Confort WW. Ultrafilters: some old and some new results. Bull Amer Math Soc 1977;83:417-55.
International Journal of Modern Computation, Information and Communication Technology