Displaying similar documents to “Maximal n-disjointed sets and the axiom of choice”

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

Horst Herrlich, Kyriakos Keremedis (1999)

Commentationes Mathematicae Universitatis Carolinae

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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.