Products, the Baire category theorem, and the axiom of dependent choice
Herrlich, Horst ; Keremedis, Kyriakos
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 771-775 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1999-01-01
Classification:  03E25,  04A25,  54A35,  54B10,  54D30,  54E52 
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     author = {Horst Herrlich and Kyriakos Keremedis},
     title = {Products, the Baire category theorem, and the axiom of dependent choice},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {771-775},
     zbl = {1010.03037},
     mrnumber = {1756551},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119129}
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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) pp. 771-775. http://gdmltest.u-ga.fr/item/119129/

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