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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

A normal countably compact not absolutely countably compact space

Author(s): Oleg Pavlov
Journal: Proc. Amer. Math. Soc. 129 (2001), 2771-2775.
MSC (1991): Primary 54D30, 54G20
Posted: April 16, 2001
MathSciNet review: 1838801
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Abstract | References | Similar articles | Additional information

Abstract:

We construct an example of a normal countably compact not absolutely countably compact space. We also prove that every hereditarily normal countably compact space is absolutely countably compact and suggest a method for construction of hereditarily normal spaces without property $(a)$.

References:

[Eng]
Ryszard Engelking, General Topology, Heldermann Verlag, Berlin, 1989. MR 91c:54001

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Fleischman W. M., A new extension of countable compactness, Fund. Math. 67 (1970), 1-9. MR 41:9200

[JMS]
Winfried Just, Michael V. Matveev, and Paul J. Szeptycki, Some results on property $(a)$, preprint.

[Mat1]
Michael V. Matveev, Absolutely countably compact spaces, Topology Appl. 58 (1994), 81-92. MR 95e:54035

[Mat2]
Michael M. Matveev, Some questions on property $(a)$, Questions Answers Gen. Topology 15 (1997), 103-111. MR 98k:54035

[Pac]
W. Pack, Absolutely countably compact topological groups, preprint.

[RSV]
Mary Ellen Rudin, Ian S. Stares and Jerry E. Vaughan, From countable compactness to absolute countable compactness, Proc. Amer. Math. Soc 125 (1997), 927-934. MR 98c:54017

[Vau]
Jerry E. Vaughan, On the product of a compact space with an absolutely countably compact space, Proceedings of the Papers on General Topology and Applications, New York Academy of Sciences 788 (1996), 203-208. MR 98g:54046

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Additional Information:

Oleg Pavlov
Affiliation: Department of Mathematics, Ohio University, Morton Hall, Athens, Ohio 45701-2979
Email: opavlov@bing.math.ohiou.edu

DOI: 10.1090/S0002-9939-01-05784-7
PII: S 0002-9939(01)05784-7
Keywords: Countably compact, absolutely countably compact, normal, hereditarily normal, property $(a)$
Received by editor(s): April 4, 1998
Received by editor(s) in revised form: November 9, 1999
Posted: April 16, 2001
Communicated by: Alan Dow
Copyright of article: Copyright 2001, American Mathematical Society




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