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

Hueytzen J. Wu, Wan-Hong Wu

Department of Mathematics, Texas A & M University—Kingsville, Kingsville, USA.
University of Texas at San Antonio, One UTSA Circle, San Antonio, USA.

DOI: 10.4236/apm.2012.24039                

Abstract

By means of a characterization of compact spaces in terms of open C_D^*-filters induced by a , a - and open C_D^*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding Y as a dense subspace of , Y_S = {ε |ε is an open C_D^*-filter that does not converge in Y}, Y_T = {A|A is a basic open C_D^*-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* = {F∈Y_s^w (or Y_T^w)|U∈F}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space X can be obtained from a by the similar process in Sec.3.

Keywords

Net; Open Filter; Open C_D*-Filter Base; Basic Open C_D*-Filter; Open C_D*-Filter; -Filter; x-Filter; Tychonoff Space; Normal T₁-Space; Compact Space; Compactifications; Stone-Cech Compactification; Wallman Compactification

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.