A countably compact space and its products

Vaughan, J. E.

doi:10.1090/S0002-9939-1978-0474206-8

A countably compact space and its products
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Proc. Amer. Math. Soc. 71 (1978), 133-137 Request permission

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 $\omega$.

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Another point in

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