Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-24T17:18:01.988Z Has data issue: false hasContentIssue false
  • English
  • Français

Borel Sets in Metric Spaces With Small Separable Subsets

Published online by Cambridge University Press:  20 November 2018

P. Daniels  and
G. Gruenhage
P. Daniels
Affiliation:
Department of Mathematics Auburn University Auburn, AL 36849
G. Gruenhage
Affiliation:
Department of Mathematics Auburn University Auburn, AL 36849
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X be a metric space such that every separable subspace of X has size less than the continuum. We answer a question of D. H. Fremlin by showing that MA + ┐CH does not necessarily imply that every subset of X is analytic.

Keywords

54H05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 471 - 475
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Amer, Beslagic, A Dowker Product, Trans. Amer. Math. Soc. 292 (1985), pp. 519–530.Google Scholar
2. Fleissner, W.G., Applications of stationary sets in topology, in Surveys in General Topology, edited by Reed, G.M., Academic Press, 1980.Google Scholar
3. Fleissner, W.G., An axiom for nonseparable Borel theory, Trans. Amer. Math. Soc. 251 (1979), pp. 309–328.Google Scholar
4. Fremlin, D.H., Note of August, ‘83, question BQ.Google Scholar
5. Ken, Kunen, Set Theory, North Holland, Amsterdam, 1980.Google Scholar
6. Miller, A., On the length of Borel hierarchies, Annals Math. Logic 16 (1979), pp. 233–267.Google Scholar
7. Stone, A.H., Non-separable Bore! sets, Dissertationes Math. 18, 1962.Google Scholar
8. Stone, A.H., Non-separable Borel sets II, Gen. Topology Appl. 2 (1972), pp. 249–270.Google Scholar