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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A normal countably compact not absolutely countably compact space


Author: Oleg Pavlov
Journal: Proc. Amer. Math. Soc. 129 (2001), 2771-2775
MSC (1991): Primary 54D30, 54G20
Published electronically: April 16, 2001
MathSciNet review: 1838801
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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 $(a)$.


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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: http://dx.doi.org/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
Published electronically: April 16, 2001
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society