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

 

Reflecting point-countable families


Author: Zoltan T. Balogh
Journal: Proc. Amer. Math. Soc. 131 (2003), 1289-1296
MSC (2000): Primary 54E35, 54A35, 54D20
Published electronically: July 25, 2002
MathSciNet review: 1948122
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Abstract: It is shown that if every $\leq \omega _{1}$-sized subspace of a (regular) space $X$ of density $\leq \omega _{1}$ has a point-countable base, then so does $X$. Similar results hold for meta-Lindelöfness. Dow's reflection theorem and a number of other results are deduced as corollaries and applications.


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Additional Information

Zoltan T. Balogh
Affiliation: Department of Mathematics & Statistics, Miami University, Oxford, Ohio 45056
Email: baloghzt@muohio.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06621-2
PII: S 0002-9939(02)06621-2
Keywords: Point-countable, reflection
Received by editor(s): July 31, 2001
Received by editor(s) in revised form: November 2, 2001
Published electronically: July 25, 2002
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society