The status of the Baire Category Theorem in ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) is investigated. Typical results: 1. The Baire Category Theorem holds for compact pseudometric spaces. 2. The Axiom of Countable Choice is equivalent to the Baire Category Theorem for co
✦ LIBER ✦
On “Subcompactness and the Baire category theorem”
✍ Scribed by Isidore Fleischer
- Book ID
- 108495266
- Publisher
- Elsevier Science
- Year
- 1979
- Weight
- 185 KB
- Volume
- 82
- Category
- Article
- ISSN
- 1385-7258
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## Abstract We show that the statement (K12) “separable, countably compact, regular spaces are Baire” is deducible from a strictly weaker form than AC, namely, CAC(ℝ) (the axiom of choice for countable families of non‐empty subsets of the real line ℝ). We also find some characterizations of the axi