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

 

A Moore space with a $\sigma$-discrete $\pi$-base
which cannot be densely embedded
in any Moore space with the Baire property


Author: David L. Fearnley
Journal: Proc. Amer. Math. Soc. 127 (1999), 3095-3100
MSC (1991): Primary 54D20, 54D25; Secondary 54E52
Published electronically: April 23, 1999
MathSciNet review: 1605960
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Abstract | References | Similar Articles | Additional Information

Abstract: The author answers a question raised in the literature about twenty five years ago and raised again more recently in Open Problems in Topology, by G. M. Reed, concerning the conjecture that every Moore space with a $ \sigma$-discrete $\pi$-base can be densely embedded in a Moore space having the Baire property. Even though closely related results have made this conjecture seem likely to be true, the author shows that, surprisingly, the conjecture is false.


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Additional Information

David L. Fearnley
Affiliation: Mathematics Institute, 24-29 St. Giles, Oxford University, Oxford OX1 3LB, England
Address at time of publication: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: david.fearnley@st-edmund-hall.oxford.ac.uk, davidf@math.byu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04876-5
PII: S 0002-9939(99)04876-5
Keywords: Moore space, $\sigma$-discrete $\pi$-base, Baire property, embedding
Received by editor(s): June 23, 1997
Received by editor(s) in revised form: December 12, 1997
Published electronically: April 23, 1999
Additional Notes: This material is based on work supported under a National Science Foundation Graduate Fellowship
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society