A Modified Wallman Method of Compactification

DOI: 10.4236/apm.2013.36076   PDF   HTML     2,552 Downloads   4,004 Views  

Abstract

Closed and basic closed C*D-filters are used in a process similar to Wallman method for compactifications of the topological spaces Y, of which, there is a subset of C*(Y) containing a non-constant function, where C*(Y) is the set of bounded real continuous functions on Y. An arbitrary Hausdorff compactification (Z,h) of a Tychonoff space X can be obtained by using basic closed C*D-filters from in a similar way, where C(Z) is the set of real continuous functions on Z.

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H. Wu and W. Wu, "A Modified Wallman Method of Compactification," Advances in Pure Mathematics, Vol. 3 No. 6, 2013, pp. 590-597. doi: 10.4236/apm.2013.36076.

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 a C*D-Base by a Modified Wallman Method,” Topology and its Applications, Vol. 155, No. 11, 2008, pp. 1163-1168. doi:10.1016/j.topol.2007.05.021

  
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