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From countable compactness to absolute countable compactness
Author(s):
Mary
Ellen
Rudin;
Ian
S.
Stares;
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  , or  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.
References:
- 1.
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- 5.
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- Peter Fletcher and William F. Lindgren, Quasi-uniform Spaces, Marcel Dekker, New York 1982. MR 84h:54026
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- Jerry E. Vaughan, On the product of a compact space with an absolutely countably compact space, to appear in the Proceedings of the Vrije University Topology Conference, Amsterdam, 1994.
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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
Affiliation:
Department of Mathematical Sciences, University of North Carolina at Greensboro Greensboro, North Carolina 27412
Email:
vaughanj@steffi.uncg.edu
DOI:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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