Ultrafilter Spaces and Compactifications

Sergio Salbany

Abstract: In this paper we shall describe a method for generating compactifications of topological spaces. We also show that standard compactifications, such as the Cech-Stone compactification and the $T_{0}$-stable compactification, can be obtained from the compactification discussed here by rendering it $T_{2}$ and $T_{0}$, respectively.

Keywords: Ultrafilter; ultrafilter spaces; compactifications; compact; locally compact; supersober spaces; $T_{0}$ stable compactification; Wallman compactification, Cech-Stone compactification; bitopological compactifications.

Classification (MSC2000): 54J05, 54D35, 54D60.

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