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

 

Baire and Volterra spaces


Authors: Gary Gruenhage and David Lutzer
Journal: Proc. Amer. Math. Soc. 128 (2000), 3115-3124
MSC (2000): Primary 54E52; Secondary 54E20, 54E25, 54E30, 54E35, 54H05, 54F65
Published electronically: March 2, 2000
MathSciNet review: 1664398
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Abstract: In this paper we describe broad classes of spaces for which the Baire space property is equivalent to the assertion that any two dense $G_{\delta }$-sets have dense intersection. We also provide examples of spaces where the equivalence does not hold. Finally, our techniques provide an easy proof of a new internal characterization of perfectly meager subspaces of $[0,1]$ and characterize metric spaces that are always of first category.


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Additional Information

Gary Gruenhage
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849-5310
Email: garyg@mail.auburn.edu

David Lutzer
Affiliation: Department of Mathematics, College of William & Mary, Williamsburg, Virginia 23187
Email: lutzer@math.wm.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05346-6
PII: S 0002-9939(00)05346-6
Keywords: Baire space, Volterra space, metric space, Moore space, Lasnev space, linearly ordered topological space, perfectly meager set, $\lambda $-set, always first category.
Received by editor(s): May 18, 1998
Received by editor(s) in revised form: November 24, 1998
Published electronically: March 2, 2000
Additional Notes: Research of the first author partially supported by NSF grant DMS-9704849, Auburn University.
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society