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

DOI:
https://doi.org/10.1090/S0002-9939-99-04780-2

Published electronically:
April 8, 1999

MathSciNet review:
1487353

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Abstract | References | Similar Articles | Additional Information

Abstract: Let us assume that Martin's Axiom holds. We prove that if is a metrizable space whose product with every Lindelöf space is Lindelöf, then for every metric on consistent with the topology of is a countable union of totally bounded subsets.

**[A1]**K. Alster,*On the product of a Lindelöf space with the space of irrationals,*Proc. Amer. Math. Soc. 110 (1990), 543-547. MR**90m:54012****[A2]**K. Alster,*Some remarks concerning the Lindelöf property of the product of a Lindelöf space with the irrationals*, Topology and its Applications 44 (1992), 19-25. MR**93g:54013****[E]**R. Engelking,*General Topology,*Heldermann Verlag, Berlin, 1989. MR**91c:54001****[K1]**A.S. Kechris,*Classical Descriptive Set Theory,*Graduate Texts in Math., vol. 156, Springer-Verlag, Berlin, 1995. MR**96e:03057****[K2]**K. Kunen,*Set theory*:*An introduction to independence proofs,*Stud. Logic Foundations Math., vol. 102, North-Holland, Amsterdam, 1980. MR**82f:03001**

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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:
https://doi.org/10.1090/S0002-9939-99-04780-2

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