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Proceedings of the American Mathematical Society

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A countably compact space and its products


Author: J. E. Vaughan
Journal: Proc. Amer. Math. Soc. 71 (1978), 133-137
MSC: Primary 54D30
MathSciNet review: 0474206
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Abstract: It is known that if a topological space X is totally countably compact, then (a) $ {X^{{\omega _1}}}$ (the product of $ {\omega _1}$ copies of X) is countably compact, and (b) for every countably compact space Y, the product $ X \times Y$ is countably compact. The main result of this paper is the construction of a space which satisfies (a) and (b), and is not totally countably compact. The example is $ X = \beta (\omega )\backslash t(p)$, where $ t(p)$ is the type of a certain kind of ultrafilter on the natural numbers $ \omega $.


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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0474206-8
Keywords: Countably compact, pseudocompact, r-compactness, totally countably compact, Rudin-Keisler order, types, P-points
Article copyright: © Copyright 1978 American Mathematical Society