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The Baire Category Theorem and choice

✍ Scribed by Horst Herrlich; Kyriakos Keremedis

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 95 KB
Volume: 108
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00132-7

No coin nor oath required. For personal study only.

✦ Synopsis

The status of the Baire Category Theorem in ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) is investigated.

Typical results:

The Baire Category Theorem holds for compact pseudometric spaces.
The Axiom of Countable Choice is equivalent to the Baire Category Theorem for countable products of compact pseudometric spaces.
The Axiom of Dependent Choice is equivalent to the Baire Category Theorem for countable products of compact Hausdorff spaces.
The Baire Category Theorem for B-compact regular spaces is equivalent to the conjunction of the Axiom of Dependent Choice and the Weak Ultrafilter Theorem.

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