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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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References

1.Burke, D. K.. On subparacompact spaces. Proc. Amer. Math. Soc., 23 (1969), 655–663.CrossRefGoogle Scholar
2.Engelking, R.. General Topology (Polish Scientific Publishers, Warsaw, 1977).Google Scholar
3.Frolik, Z.. On the topological product of paracompact spaces. Bull. Acad. Pol., Sci. Ser. Math., 8 (1960), 747–750.Google Scholar
4.Frolik, Z. and Holicky, P.. Non-separable analytic spaces and measurable correspondences. Uspehi Mat. Nauk., 35: 3 (1980), 37–43, or Russian Math. Surveys, 35: 3 (1980), 41-48.Google Scholar
5.Frolik, Z. and Holicky, P.. Selections using orderings (non-separable case). Comment. Math. Univ. Camlin., 21 (1980), 653–661.Google Scholar
6.Frolik, Z. and Holicky, P.. Decomposability of completely Suslin-additive families. Proc. Amer. Math. Soc., 82 (1981), 359–365.CrossRefGoogle Scholar
7.Frolik, Z. and Holický, P.. Analytic and Luzin spaces (non-separable case). Preprint.Google Scholar
8.Frolik, Z. and Holický, P.. Applications of Luzinian separation principles (non-separable case). Fund. Math., 118 (1983), 165–185.CrossRefGoogle Scholar
9.Hansell, R. W.. On the representation of nonseparable analytic sets. Proc. Amer. Math. Soc., 39 (1973), 402 408.CrossRefGoogle Scholar
10.Hansell, R. W.. On characterizing non-separable analytic and extended Borel sets as types of continuous images. Proc. London Math. Soc., (3), 28 (1974), 683–699.CrossRefGoogle Scholar
11.Hansell, R. W., Jayne, J. E. and Rogers, C. A.. Separation theorems for K-analytic sets. To appear, perhaps in Mathematika.Google Scholar
12.Holický, P.. Neseparabilni analytiké prostory (Non-separable analytic spaces). CSc Thesis (Charles University, Prague, 1977).Google Scholar
13.Holicky, P.. Remark on completely Baire-additive families in analytic spaces. Comment. Math. Univ. Carotin., 22 (1981), 327–336.Google Scholar
14.Kelly, J. L.. General Topology (Van Nostrand Reinhold, New York, 1955).Google Scholar
15.Rogers, C. A., Jayne, J. E., Dellacherie, C., Topsøe, F., Hoffmann-Jørgensen, J., Martin, D. A., Kechris, A. S. and Stone, A. H.. Analytic Sets (Academic Press, London, 1980).Google Scholar
16.HANSELL, R. W.. Borel measurable mappings for non-separable metric spaces. Trans. Amer. Math. Soc., 161 (1971), 145–169.CrossRefGoogle Scholar
17.HANSELL, R. W.. On the non-separable theory of Borel and Souslin sets. Bull. Amer. Math. Soc., 78 (1972), 236–242.CrossRefGoogle Scholar
18.HANSELL, R. W.. On the non-separable theory of k-Borel and K-Souslin sets. Gen. Top. and Appl, 3 (1972), 161–195.CrossRefGoogle Scholar
19.HANSELL, R. W.. On Baire functions and Borel mappings. Trans. Amer. Math. Soc., 194 (1974), 195–211.CrossRefGoogle Scholar
20.HANSELL, R. W.. Hereditarily-additive families in descriptive set theory and Borel measurable multimaps. Trans. Amer. Math. Soc., 278 (1983), 725–749.Google Scholar