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Open covers and the square bracket
partition relation

Author: Marion Scheepers
Journal: Proc. Amer. Math. Soc. 125 (1997), 2719-2724
MSC (1991): Primary 03E05
MathSciNet review: 1396995
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Abstract: An open cover ${\cal U}$ of an infinite separable metric space $X$ is an $\omega $-cover of $X$ if $X\not \in{\cal U}$ and for every finite subset $F$ of $X$ there is a $U\in {\cal U}$ such that $F\subseteq U$. Let $\Omega $ be the collection of $\omega $-covers of $X$. We show that the partition relation $\Omega \rightarrow[\Omega ]^2_2$ holds if, and only if, the partition relation $\Omega \rightarrow[\Omega ]^2_3$ holds.

References [Enhancements On Off] (What's this?)

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Additional Information

Marion Scheepers
Affiliation: Department of Mathematics and Computer Science Boise State University Boise, Idaho 83725

Keywords: Rothberger property, square bracket partition relation, Ramsey's theorem
Received by editor(s): October 13, 1995
Received by editor(s) in revised form: April 11, 1996
Additional Notes: The author was supported by NSF grant DMS 95 - 05375
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society

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