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

 

Lindelöf spaces concentrated on Bernstein subsets of the real line


Author: L. Brian Lawrence
Journal: Proc. Amer. Math. Soc. 114 (1992), 211-215
MSC: Primary 54D20; Secondary 54E50
MathSciNet review: 1062832
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Abstract: We show in ZFC that for each $ n$ with $ n \in \omega $ or $ n = \omega $, there is a Lindelöf space $ X$ and a separable metric space $ M$ such that for every $ m < n$, $ X \times {}^mM$ is Lindelöf, whereas $ X \times {}^nM$ is nonnormal.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1062832-4
PII: S 0002-9939(1992)1062832-4
Keywords: Product, separable metric space, Lindelöf space, normal, concentrated, Bernstein set
Article copyright: © Copyright 1992 American Mathematical Society