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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
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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

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