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Analytic sets in Hausdorff spaces

Published online by Cambridge University Press:  26 February 2010

C. A. Rogers
C. A. Rogers
Affiliation:
University College, London
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When Souslin and Lusin initiated and developed the theories of the Souslin operation, of projective sets and of analytic sets, they attached great importance to the constructive nature of their definitions (see [1], [2] and [3]). When Choquet (see [4], [5] and [6]) made his very successful extension of these theories to an arbitrary Hausdorff space Ω, he defined an analytic set in Ω to be a continuous image in Ω of a Kσδ-set in an unspecified compact Hausdorff space X. Thus, a priori, the construction of the analytic sets in Ω requires the preliminary construction of all compact Hausdorff spaces X.

Type
Research Article
Information
Mathematika , Volume 11 , Issue 1 , June 1964 , pp. 1 - 8
Copyright
Copyright © University College London 1964

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References

1.Souslin, M., “Sur une définition des ensembles mesurables B sans nombres transfinis”, C.R. Acad. Sci. Paris, 164 (1917), 88.Google Scholar
2.Lusin, N., Les ensembles analytiques (Paris, 1930).Google Scholar
3.Sierpiński, W., “Les ensembles projectifs et analytiques”, Mém. Sci. Math., 112 (Paris, 1950).Google Scholar
4.Choquet, G., “Ensembles boréliens et analytiques dans les espaces topologiques”, C.R. Acad. Sci. Paris, 232 (1951), 2174–2176.Google Scholar
5.Choquet, G., “Theory of capacities”, Ann. Inst. Fourier, Grenoble, 5 (1953–1954), 131–295.CrossRefGoogle Scholar
6.Choquet, G., “Ensembles K-analytiques et K-sousliniens”, Ann. Inst. Fourier, Grenoble, 9 (1959), 75–89.Google Scholar
7.Sion, M., “On analytic sets in topological spaces”, Trans. American Math. Soc, 96 (1960), 341–354.Google Scholar
8.Sion, M., “Topological and measure theoretical properties of analytic sets”, Proc, American Math. Soc, 11 (1960), 769–776.Google Scholar
9.Sion, M., “Continuous images of Borel sets”, Proc. American Math. Soc, 12 (1961), 385–391.Google Scholar
10.Kelley, J. L., General topology (New York, 1955).Google Scholar
11.Frolik, Z., “On the descriptive theory of sets”, Czech. Math. J., 13 (88), (1963), 335–359.Google Scholar
12.Frolik, Z., “On bianalytic spaces”, Czech. Math. J., 13 (88), (1963), 561–573.Google Scholar
13.Bressler, D. W. and Sion, M., “The current theory of analytic sets”, Canadian J. Math., 16 (1964), 207–230.Google Scholar