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Baire and Volterra spaces
Author(s):
Gary
Gruenhage;
David
Lutzer
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3115-3124.
MSC (2000):
Primary 54E52;
Secondary 54E20, 54E25, 54E30, 54E35, 54H05, 54F65
Posted:
March 2, 2000
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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  -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 ![$[0,1]$](/proc/2000-128-10/S0002-9939-00-05346-6/gif-abstract0/img2.gif) and characterize metric spaces that are always of first category.
References:
- [AN]
- Arhangel'skii, A. and Nedev, S., Some remarks on semi- metrizable spaces and their subspaces, Comptes Rendu Acad. Bulgare Sci., 31(1978), 499-500. MR 80c:54026
- [BHL]
- Bennett, H., Hosobuchi, M., and Lutzer, D., On weakly perfect generalized ordered spaces, to appear.
- [vD]
- van Douwen, E. K., Applications of maximal topologies, Topology and its Applications, 51 (1993), 125-139. MR 94h:54012
- [E]
- Engelking, R., General Topology, Heldermann Verlag, Berlin, 1989. MR 91c:54001
- [G1]
- Gruenhage, G., Generalized metric spaces, pp. 425-501, in Handbook of Set Theoretic Topology, ed. by Kunen, K., and Vaughan, J., North Holland, 1984, Amsterdam. MR 86h:54038
- [G2]
- Gruenhage, G., Irreducible restrictions of closed mappings, 8th Prague Topological Symposium on General Topology and Its Relations to Modern Analysis and Algebra (1996). Topology Appl. 85 (1998), no. 1-3, 127-135. CMP 98:11
- [GGP]
- Gauld, D., Greenwood, D., and Piotrowski, Z., On Volterra spaces II, Annals of the New York Academy of Sciences, 806 (1996), 169-173. MR 97m:54052
- [GP]
- Gauld, D., and Piotrowski, Z., On Volterra spaces, Far East J. Math. Sci. 1 (1993), 209-214. MR 94k:54070
- [H]
- Hewitt, E. A problem of set-theoretic topology, Duke Math J. 10(1943), 309-333. MR 5:46e
- [He]
- Heath, R.W., Screenability, pointwise paracompactness, and metrization of Moore spaces, Canad. J. Math 16 (1964), 763-770. MR 29:4033
- [K]
- Kuratowski, K., Topology, Volume 1, Academic Press, 1966, New York. MR 36:840
- [P]
- Pytkeev, E.G., Maximally resolvable spaces, Trudy Mat. Inst. Steklov, 154 (1983), 209-213. MR 85c:54039
- [RM]
- Reed, G.M. and McIntyre, D.W., A Moore space with caliber (
 ) but without caliber  , Topology and its Applications, 44 (1992), 325-329. MR 93i:54019 - [T]
- Todorcevic, S., Trees and linearly ordered sets, pp. 235-293, in Handbook of Set Theoretic Topology, ed. by Kunen, K., and Vaughan, J., North Holland, 1984, Amsterdam. MR 86h:54040
- [V]
- Volterra, V., Alcune osservasioni sulle funzioni punteggiate discontinue, Giornale di Matematiche 19 (1881), 76-86.
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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:
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
Posted:
March 2, 2000
Additional Notes:
Research of the first author partially supported by NSF grant DMS-9704849, Auburn University.
Communicated by:
Alan Dow
Copyright of article:
Copyright
2000,
American Mathematical Society
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