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

 

A Lindelöf space with no Lindelöf subspace of size $\aleph_1$


Authors: Piotr Koszmider and Franklin D. Tall
Journal: Proc. Amer. Math. Soc. 130 (2002), 2777-2787
MSC (2000): Primary 54A20, 54A25, 54A35; Secondary 03E35
Published electronically: March 13, 2002
MathSciNet review: 1900885
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Abstract: A consistent example of an uncountable Lindelöf $T_3$ (and hence normal) space with no Lindelöf subspace of size $\aleph_1$is constructed. It remains unsolved whether extra set-theoretic assumptions are necessary for the existence of such a space. However, our space has size $\aleph_2$and is a $P$-space, i.e., $G_\delta$'s are open, and for such spaces extra set-theoretic assumptions turn out to be necessary.


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Additional Information

Piotr Koszmider
Affiliation: Departamento de Matemática, Universidade de São Paulo, Caixa Postal: 66281, São Paulo, SP, CEP: 05315-970, Brasil
Email: piotr@ime.usp.br

Franklin D. Tall
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: tall@math.toronto.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06367-0
PII: S 0002-9939(02)06367-0
Keywords: Lindel\"of, nonreflection
Received by editor(s): December 12, 2000
Received by editor(s) in revised form: April 2, 2001
Published electronically: March 13, 2002
Additional Notes: Both authors were partially supported by the second author’s grant A-7354 from the Natural Sciences and Engineering Research Council of Canada
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society