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Proceedings of the American Mathematical Society

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Wallman-type compactifications and products


Author: Frank Kost
Journal: Proc. Amer. Math. Soc. 29 (1971), 607-612
MSC: Primary 54.53
DOI: https://doi.org/10.1090/S0002-9939-1971-0281159-8
MathSciNet review: 0281159
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Abstract: Y is a Wallman-type compactification (O. Frink, Amer. J. Math. 86 (1964), 602-607) of X in case there is a normal base Z for the closed sets of X such that the ultrafilter space from Z, denoted $ \omega (Z)$, is topologically Y. It is not known if every compactification is Wallman-type. For $ {Z_\alpha }$ a normal base for the closed sets of $ {X_\alpha }$ for each a belonging to an index set $ \Delta $ it is shown that the Tychonoff product space $ {\prod _{\alpha \in \Delta }}\omega ({Z_\alpha })$ is a Wallman compactification of $ {\prod _{\alpha \in \Delta }}{X_\alpha }$. Also for $ X \subset T \subset \omega (Z)$ with Z a normal base for the closed sets of X, a proof that $ \omega (Z)$ is a Wallman-type compactification of T is indicated.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0281159-8
Keywords: Wallman-type compactification, normal base, zero set, free ultrafilter
Article copyright: © Copyright 1971 American Mathematical Society

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