A Lindelöf space with no Lindelöf subspace of size $\aleph _1$
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- by Piotr Koszmider and Franklin D. Tall PDF
- Proc. Amer. Math. Soc. 130 (2002), 2777-2787 Request permission
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.References
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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
- MR Author ID: 170400
- Email: tall@math.toronto.edu
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1900885