Open covers and the square bracket

partition relation

Author:
Marion Scheepers

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2719-2724

MSC (1991):
Primary 03E05

DOI:
https://doi.org/10.1090/S0002-9939-97-03898-7

MathSciNet review:
1396995

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Abstract | References | Similar Articles | Additional Information

Abstract: An open cover of an infinite separable metric space is an -cover of if and for every finite subset of there is a such that . Let be the collection of -covers of . We show that the partition relation holds if, and only if, the partition relation holds.

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Additional Information

**Marion Scheepers**

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

Email:
marion@math.idbsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03898-7

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