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

 

Some remarks on metric spaces
whose product with every Lindelöf space
is Lindelöf


Author: K. Alster
Journal: Proc. Amer. Math. Soc. 127 (1999), 2469-2473
MSC (1991): Primary 54B10, 54D20
Published electronically: April 8, 1999
MathSciNet review: 1487353
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Abstract: Let us assume that Martin's Axiom holds. We prove that if $X$ is a metrizable space whose product with every Lindelöf space is Lindelöf, then for every metric $d$ on $X,$ consistent with the topology of $X, (X,d)$ is a countable union of totally bounded subsets.


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Additional Information

K. Alster
Affiliation: Institute of Mathematics, Polish Academy of Sciences, 00-950 Warsaw, Poland
Email: kalster@impan.gov.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04780-2
PII: S 0002-9939(99)04780-2
Keywords: Metric spaces, product, Lindel\"of spaces
Received by editor(s): November 12, 1996
Received by editor(s) in revised form: October 31, 1997
Published electronically: April 8, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society