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) (the product of copies of *X*) is countably compact, and (b) for every countably compact space *Y*, the product 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 , where is the type of a certain kind of ultrafilter on the natural numbers .

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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