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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Partitioning topological spaces into countably many pieces


Authors: P. Komjáth and W. Weiss
Journal: Proc. Amer. Math. Soc. 101 (1987), 767-770
MSC: Primary 54A25; Secondary 04A20, 05A17
DOI: https://doi.org/10.1090/S0002-9939-1987-0911048-6
MathSciNet review: 911048
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Abstract: We assume $ X \to (\operatorname{top}\omega + 1)_\omega ^1$ and determine which larger $ \alpha $ can replace $ \omega + 1$. If $ X$ is first countable, any countable $ \alpha $ can replace $ \omega + 1$. If the character of $ X$ is $ {\omega _1}$, it is consistent and independent whether $ {\omega ^2} + 1$ can always replace $ \omega + 1$. Consistently $ {\omega _1}$ cannot replace $ \omega + 1$ for any $ X$ of size $ {\omega _1}$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0911048-6
Keywords: Partition, diamond, countable ordinal
Article copyright: © Copyright 1987 American Mathematical Society