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# Wallman-Type Compactifications on 0-Dimensional Spaces

Li Pi Su
Proceedings of the American Mathematical Society
Vol. 43, No. 2 (Apr., 1974), pp. 455-460
DOI: 10.2307/2038913
Stable URL: http://www.jstor.org/stable/2038913
Page Count: 6
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## Abstract

Let E be Hausdorff 0-dimensional, D the discrete space {0, 1}, and N the discrete space of all nonnegative integers. Every E-completely regular space X has a clopen normal base F with $X\backslash F \in \mathscr{F}$ for each F ∈ F. The Wallman compactification ω(F) is D-compact. Moreover, if an E-completely regular space X has a countably productive clopen normal base F with $X\backslash F \in \mathscr{F}$ for each F ∈ F, then the Wallman space η(F) is N-compact. Hence, if X has such an F, and is an F-realcompact space, then X is N-compact.

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