Hostname: page-component-74656f9884-g96k6 Total loading time: 0 Render date: 2026-11-11T00:02:31.880Z Has data issue: false hasContentIssue false
  • English
  • Français

K-analytic spaces with metrizable compacta

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  26 February 2010

D. H. Fremlin
D. H. Fremlin
Affiliation:
University of Essex, Colchester, Essex.
Get access

Extract

I discuss various necessary and sufficient conditions for a K-analytic space to be Souslin. In particular, I show that if the continuum hypothesis is true, then there is a non-Souslin K-analytic space in which every compact set is metrizable; while if Martin's Axiom is true and the continuum hypothesis is false, this is impossible.

MSC classification

Secondary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)

Information

Type
Research Article
Information
Mathematika , Volume 24 , Issue 2 , December 1977 , pp. 257 - 261
Copyright
Copyright © University College London 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Bressler, D. W. and Sion, M.. “The current theory of analytic sets”, Canad. J. Math., 16 (1964), 207–230.Google Scholar
2.Choquet, G.. Lectures in Analysis (Benjamin, 1969)Google Scholar
3.Frohik, Z.. “Analytic and borelian sets in general spaces”, Proc. London Math. Soc. (3), 21 (1970), 674–692.Google Scholar
4.Frolik, Z.. “A survey of separable descriptive theory of sets and spaces”, Czech. Math. J., 20 (1970), 406–467.CrossRefGoogle Scholar
5.Golomb, S. W.. “A connected topology for the integers”, Amer. Math. Monthly, 66 (1959), 663–665.Google Scholar
6.Jayne, J. E.. “Structure of analytic Hausdorff spaces”, Mathematika, 23 (1976), 208–211.Google Scholar
7.Martin, D. A. and Solovay, R. M.. “Internal Cohen extensions”, Ann. Math. Logic, 2 (1970), 143–178.Google Scholar
8.Rogers, C. A.. “Analytic sets in Hausdorff spaces”, Mathematika, 11 (1964), 1–8.Google Scholar
9.Rosenthal, H. P.. “The heredity problem for weakly compactly generated Banach spaces”, Comp. Math., 28 (1974), 83–111.Google Scholar
10.Rudin, M. E.. “Martin's Axiom”; §B6 of Handbook of Mathematical Logic, ed. Barwise, J. (North-Holland, 1977).Google Scholar
11.Schwartz, L.. Radon measures on arbitrary topological spaces and cylindrical measures (Oxford U.P., 1973).Google Scholar
12.Talagrand, M.. “Sur la structure borélienne des espaces analytiques” (to appear).Google Scholar
13.Talagrand, M.. “spaces de Banach faiblement. K-analytiques” (to appear).Google Scholar