A Lindelöf space with no Lindelöf subspace of size

Authors:
Piotr Koszmider and Franklin D. Tall

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2777-2787

MSC (2000):
Primary 54A20, 54A25, 54A35; Secondary 03E35

DOI:
https://doi.org/10.1090/S0002-9939-02-06367-0

Published electronically:
March 13, 2002

MathSciNet review:
1900885

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Abstract | References | Similar Articles | Additional Information

Abstract: A consistent example of an uncountable Lindelöf (and hence normal) space with no Lindelöf subspace of size is constructed. It remains unsolved whether extra set-theoretic assumptions are necessary for the existence of such a space. However, our space has size and is a -space, i.e., '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:
https://doi.org/10.1090/S0002-9939-02-06367-0

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