Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Lusin sets

Author(s): Marion Scheepers
Journal: Proc. Amer. Math. Soc. 127 (1999), 251-257.
MSC (1991): Primary 90D44
MathSciNet review: 1458261
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Abstract: We show that a set of real numbers is a Lusin set if, and only if, it has a covering property similar to the familiar property of Rothberger

References:

1.: F. Galvin and A.W. Miller, $\gamma$ -sets and other singular sets of real numbers, Topology and its Applications 17 (1984), 145 - 155. MR 85f:54011
2.: W. Just, More on Lusin sets, a TeX-file identified by Just as ``version of 11/08/96 lusin3.tex''.
3.: W. Just, A.W. Miller, M. Scheepers and P.J. Szeptycki, Combinatorics of open covers (II), Topology and its Applications 73 (1996), 241 - 266. CMP 97:04
4.: K. Kunen, Random and Cohen reals, Handbook of Set Theoretic Topology, North-Holland (1984), 887 - 911. MR 86d:03049
5.: N. Lusin, Sur un problème de M. Baire, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris 158 (1914), 1258 - 1261.
6.: I. Rec{\l}aw, Every Lusin set is undetermined in Point-open game, Fundamenta Mathematicae 144 (1994), 43 - 54. MR 95f:04005
7.: F. Rothberger, Eine Verschärfung der Eigenschaft $\textsf{C}$ , Fundamenta Mathematicae 30 (1938), 50 - 55.
8.: M. Scheepers, Rothberger's property and partition relations, The Journal of Symbolic Logic, 62 (1997), 976-980.
9.: S. Willard, General Topology, Addison-Wesley Publishing Company (1970). MR 41:9173

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Additional Information:

Marion Scheepers
Affiliation: Department of Mathematics, Boise State University, Boise, Idaho 83725
Email: marion@math.idbsu.edu

DOI: 10.1090/S0002-9939-99-04512-8
PII: S 0002-9939(99)04512-8
Keywords: Lusin set, infinite game, partition relation
Received by editor(s): November 5, 1996
Received by editor(s) in revised form: May 16, 1997
Additional Notes: The author's research was funded in part by NSF grant DMS 95-05375
Communicated by: Andreas R. Blass
Copyright of article: Copyright 1999, American Mathematical Society

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