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K-analytic sets

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  26 February 2010

R. W. Hansell ,
J. E. Jayne  and
C. A. Rogers
R. W. Hansell
Affiliation:
Dept. of Mathematics, University of Connecticut, Storrs, Connecticut 06268, U.S.A.
J. E. Jayne
Affiliation:
Dept. of Mathematics, University College London, Gower Street, London. WC1E 6BT
C. A. Rogers
Affiliation:
Dept. of Mathematics, University College London, Gower Street, London. WC1E 6BT
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Extract

The classical theory of analytic sets works well in metric spaces, but the analytic sets themselves are automatically separable. The theory of K-analytic sets, developed by Choquet, Sion, Frolik and others, works well in Hausdorff spaces, but the K-analytic sets themselves remain Lindelof. The theory of k-analytic sets developed by A. H. Stone and R. W. Hansell works well in non-separable metric spaces, especially in the special case, when k is ℵ0, with which we shall be concerned, see [9, 10 and 16–20]. Of course the k-analytic sets are metrizable. For accounts of these theories, see, for example, [15].

MSC classification

Secondary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
Type
Research Article
Information
Mathematika , Volume 30 , Issue 2 , December 1983 , pp. 189 - 221
Copyright
Copyright © University College London 1983

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