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Analytic sets in Hausdorff spaces

  • C. A. Rogers (a1)
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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.

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1.Souslin, M., “Sur une définition des ensembles mesurables B sans nombres transfinis”, C.R. Acad. Sci. Paris, 164 (1917), 88.
2.Lusin, N., Les ensembles analytiques (Paris, 1930).
3.Sierpiński, W., “Les ensembles projectifs et analytiques”, Mém. Sci. Math., 112 (Paris, 1950).
4.Choquet, G., “Ensembles boréliens et analytiques dans les espaces topologiques”, C.R. Acad. Sci. Paris, 232 (1951), 21742176.
5.Choquet, G., “Theory of capacities”, Ann. Inst. Fourier, Grenoble, 5 (1953–1954), 131295.
6.Choquet, G., “Ensembles K-analytiques et K-sousliniens”, Ann. Inst. Fourier, Grenoble, 9 (1959), 7589.
7.Sion, M., “On analytic sets in topological spaces”, Trans. American Math. Soc, 96 (1960), 341354.
8.Sion, M., “Topological and measure theoretical properties of analytic sets”, Proc, American Math. Soc, 11 (1960), 769776.
9.Sion, M., “Continuous images of Borel sets”, Proc. American Math. Soc, 12 (1961), 385391.
10.Kelley, J. L., General topology (New York, 1955).
11.Frolik, Z., “On the descriptive theory of sets”, Czech. Math. J., 13 (88), (1963), 335359.
12.Frolik, Z., “On bianalytic spaces”, Czech. Math. J., 13 (88), (1963), 561573.
13.Bressler, D. W. and Sion, M., “The current theory of analytic sets”, Canadian J. Math., 16 (1964), 207230.
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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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