Geodesic
Products, the Baire category theorem, and the axiom of dependent choice
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 771-775.

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In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statements are shown to be equivalent: (i) The axiom of dependent choice. (ii) Products of compact Hausdorff spaces are Baire. (iii) Products of pseudocompact spaces are Baire. (iv) Products of countably compact, regular spaces are Baire. (v) Products of regular-closed spaces are Baire. (vi) Products of Čech-complete spaces are Baire. (vii) Products of pseudo-complete spaces are Baire.
Classification : 03E25, 04A25, 54A35, 54B10, 54D30, 54E52
Keywords: axiom of dependent choice; Baire category theorem; Baire space; (countably) compact; pseudocompact; Čech-complete; regular-closed; pseudo-complete; product spaces 
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Herrlich, Horst; Keremedis, Kyriakos. Products, the Baire category theorem, and the axiom of dependent choice. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 771-775. http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a12/