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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
DOI: https://doi.org/10.1090/S0002-9939-1992-1062832-4
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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Keywords: Product, separable metric space, Lindel&#246;f space, normal, concentrated, Bernstein set
Article copyright: © Copyright 1992 American Mathematical Society