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

 

From countable compactness to absolute countable compactness


Authors: Mary Ellen Rudin, Ian S. Stares and Jerry E. Vaughan
Journal: Proc. Amer. Math. Soc. 125 (1997), 927-934
MSC (1991): Primary 54D20; Secondary 54A35
MathSciNet review: 1415367
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Abstract: We show that every countably compact space which is monotonically normal, almost 2-fully normal, radial $T_2$, or $T_3$ with countable spread is absolutely countably compact. For the first two mentioned properties, we prove more general results not requiring countable compactness. We also prove that every monotonically normal, orthocompact space is finitely fully normal.


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Additional Information

Mary Ellen Rudin
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: mrudin@math.wisc.edu

Ian S. Stares
Affiliation: Department of Mathematical Sciences\ University of North Carolina at Greensboro\ Greensboro, North Carolina 27412
Email: isstares@maths.ox.ac.uk

Jerry E. Vaughan
Email: vaughanj@steffi.uncg.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04030-6
PII: S 0002-9939(97)04030-6
Keywords: Countably compact, absolutely countably compact, monotonically normal, property (a), finitely fully normal, almost 2-fully normal, radial, orthocompact, countable spread
Received by editor(s): September 10, 1995
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1997 American Mathematical Society