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

DOI:
https://doi.org/10.1090/S0002-9939-00-05346-6

Published electronically:
March 2, 2000

MathSciNet review:
1664398

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 -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 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:
https://doi.org/10.1090/S0002-9939-00-05346-6

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