The Baire Category Property and Some Notions of Compactness |
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Authors: | Fossy Jules; Morillon Marianne |
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Institution: | Département de Mathématiques et Informatique 15, Avenue René Cassin, Saint-Denis de la Réunion 97715, France
Département de Mathématiques et Informatique 15, Avenue René Cassin, Saint-Denis de la Réunion 97715, France E-mail: mar{at}univ-reunion.fr |
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Abstract: | We work in set theory without the axiom of choice: ZF. We showthat the axiom BC: Compact Hausdorff spaces are Baire, is equivalentto the following axiom: Every tree has a subtree whose levelsare finite, which was introduced by Blass (cf. 4]). This settlesa question raised by Brunner (cf. 9, p. 438]). We also showthat the axiom of Dependent Choices is equivalent to the axiom:In a Hausdorff locally convex topological vector space, convex-compactconvex sets are Baire. Here convex-compact is the notion whichwas introduced by Luxemburg (cf. 16]). |
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