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

 

Metacompact subspaces of products of ordinals


Author: William G. Fleissner
Journal: Proc. Amer. Math. Soc. 130 (2002), 293-301
MSC (2000): Primary 54D20; Secondary 54F05, 03E10
Published electronically: May 25, 2001
MathSciNet review: 1855648
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Abstract:

Let $X$ be a subspace of the product of finitely many ordinals. $X$ is countably metacompact, and $X$ is metacompact iff $X$ has no closed subset homeomorphic to a stationary subset of a regular uncountable cardinal. A theorem generalizing these two results is: $X$ is $\lambda$-metacompact iff $X$has no closed subset homeomorphic to a $ (\kappa_1, \ldots , \kappa_n)$-stationary set where $\kappa_1 < \lambda$.


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Additional Information

William G. Fleissner
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: fleissne@math.ukans.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06026-9
PII: S 0002-9939(01)06026-9
Keywords: Metacompact, stationary set, pressing down lemma, finite product of ordinals
Received by editor(s): March 8, 2000
Received by editor(s) in revised form: June 6, 2000
Published electronically: May 25, 2001
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society