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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 = {e |e 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 X can be obtained from a by the similar process in Sec.3.

advances in pure mathematics

A&amp;amp;zeta;x- and Open &amp;lt;i&amp;gt;C&amp;lt;sub&amp;gt;D&amp;lt;/sub&amp;gt;&amp;lt;sup&amp;gt;*&amp;lt;/sup&amp;gt;&amp;lt;/i&amp;gt;-Filters Process of Compactifications and Any Hausdorff Compactification