TITLE:
Aζx- and Open CD*-Filters Process of Compactifications and Any Hausdorff Compactification
AUTHORS:
Hueytzen J. Wu, Wan-Hong Wu
KEYWORDS:
Net; Open Filter; Open CD*-Filter Base; Basic Open CD*-Filter; Open CD*-Filter; -Filter; x-Filter; Tychonoff Space; Normal T1-Space; Compact Space; Compactifications; Stone-Cech Compactification; Wallman Compactification
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.4,
July
30,
2012
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* = {F∈Ysw (or YTw)|U∈F}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space Xcan be obtained from a by thesimilar process in Sec.3.