An example of a space which is countably compact whose square is countably paracompact but not countably compact

Author:
Lee Parsons

Journal:
Proc. Amer. Math. Soc. **65** (1977), 351-354

MSC:
Primary 54G20; Secondary 54D20

MathSciNet review:
0451218

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Abstract: A subspace *P* of is obtained whose square is disjoint from the graph, *G*, of a pre-selected homeomorphism that has no fixed points. The construction is performed in such a way that, for , all countable subsets of will have a limit point in . We use the following lemma: If is countably infinite, then .

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DOI:
https://doi.org/10.1090/S0002-9939-1977-0451218-0

Keywords:
Countably compact,
countably paracompact,
extremally disconnected,
*M*-space,
pseudocompact

Article copyright:
© Copyright 1977
American Mathematical Society