## Horst Herrlich, Kyriakos Keremedis

*Products, the Baire category theorem, and the axiom of dependent choice *

Comment.Math.Univ.Carolinae 40,4 (1999) 771-775. **Abstract:**In {ZF} (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statements are shown to be equivalent: \roster \item The axiom of dependent choice. \item Products of compact Hausdorff spaces are Baire. \item Products of pseudocompact spaces are Baire. \item Products of countably compact, regular spaces are Baire. \item Products of regular-closed spaces are Baire. \item Products of \v {C}ech-complete spaces are Baire. \item Products of pseudo-complete spaces are Baire. \endroster

**Keywords:** axiom of dependent choice, Baire category theorem, Baire space, (countably) compact, pseudocompact, \v {C}ech-complete, regular-closed, pseudo-complete, product spaces

**AMS Subject Classification:** 03E25, 04A25, 54A35, 54B10, 54D30, 54E52

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