Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A subspace P of $ \beta N - N$ is obtained whose square is disjoint from the graph, G, of a pre-selected homeomorphism $ f:\beta N \to \beta N$ that has no fixed points. The construction is performed in such a way that, for $ X = P \cup N$, all countable subsets of $ {X^2} - G$ will have a limit point in $ {X^2}$. We use the following lemma: If $ K \subset {(\beta N)^2} - G$ is countably infinite, then $ \vert{\text{cl}_{{{(\beta N)}^2}}}K - G\vert = {2^c}$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54G20, 54D20

Retrieve articles in all journals with MSC: 54G20, 54D20

Additional Information

Keywords: Countably compact, countably paracompact, extremally disconnected, M-space, pseudocompact
Article copyright: © Copyright 1977 American Mathematical Society