Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-12-02T22:09:12.521Z Has data issue: false hasContentIssue false
  • English
  • Français

THE BAIRE CATEGORY PROPERTY AND SOME NOTIONS OF COMPACTNESS

Published online by Cambridge University Press:  01 February 1998

JULES FOSSY  and
MARIANNE MORILLON
JULES FOSSY
Affiliation:
Département de Mathématiques et Informatique, 15, Avenue René Cassin, Saint-Denis de la Réunion 97715, France
MARIANNE MORILLON
Affiliation:
Département de Mathématiques et Informatique, 15, Avenue René Cassin, Saint-Denis de la Réunion 97715, France
Get access

Abstract

We work in set theory without the axiom of choice: ZF. We show that the axiom BC: Compact Hausdorff spaces are Baire, is equivalent to the following axiom: Every tree has a subtree whose levels are finite, which was introduced by Blass (cf. [4]). This settles a question raised by Brunner (cf. [9, p. 438]). We also show that the axiom of Dependent Choices is equivalent to the axiom: In a Hausdorff locally convex topological vector space, convex-compact convex sets are Baire. Here convex-compact is the notion which was introduced by Luxemburg (cf. [16]).

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 1 - 19
Copyright
The London Mathematical Society 1998

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.)