Aζx- and Open CD*-Filters Process of Compactifications and Any Hausdorff Compactification

DOI: 10.4236/apm.2012.24039   PDF   HTML     2,656 Downloads   5,165 Views  

Abstract

By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding Y as a dense subspace of , YS = {ε |ε is an open CD*-filter that does not converge in Y}, YT = {A|A is a basic open CD*-filter that does not converge in Y}, is the topology induced by the base B = {U*|U is open in Y, U φ} and U* = {FYsw (or YTw)|UF}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space X can be obtained from a by the similar process in Sec.3.

Share and Cite:

H. Wu and W. Wu, "Aζx- and Open CD*-Filters Process of Compactifications and Any Hausdorff Compactification," Advances in Pure Mathematics, Vol. 2 No. 4, 2012, pp. 296-300. doi: 10.4236/apm.2012.24039.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] S. Willard, “General Topology,” Addison-Wesley, Reading, 1970.
[2] H. J. Wu and W. H. Wu, “An Arbitrary Hausdorff Compactification of a Tychonoff Space X Obtained from CD*-Base by a Modified Wallman Method,” Topology and its Applications, Vol. 155, 2008, pp. 1163-1168. doi:10.1016/j.topol.2007.05.021
[3] J. L. Kelly, “General Topology,” Van Nostrand, Princeton, 1955.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.