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Aζx- and Open <i>C<sub>D</sub><sup>*</sup></i>-Filters Process of Compactifications and Any Hausdorff Compactification
Department of Mathematics, Texas A & M University—Kingsville, Kingsville, USA
University of Texas at San Antonio, One UTSA Circle, San Antonio, USA
- 1 Department of Mathematics, Texas A & M University—Kingsville, Kingsville, USA
- 2 University of Texas at San Antonio, One UTSA Circle, San Antonio, USA
Advances in Pure Mathematics·Volume 02 (2012)·Pages 296–300·Published 30 July 2012·DOI10.4236/apm.2012.24039
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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.
KeywordsNetOpen FilterOpen C<i><sub>D</sub></i>*-Filter BaseBasic Open C<sub>D</sub>*-FilterOpen C<sub>D</sub>*-Filter
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