Geodesic
Choice principles in elementary topology and analysis
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 545-552 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Many fundamental mathematical results fail in {\bf{ZF}}, i.e., in Zermelo-Fraenkel set theory without the Axiom of Choice. This article surveys results --- old and new --- that specify how much ``choice'' is needed {\it precisely} to validate each of certain basic analytical and topological results.
Many fundamental mathematical results fail in {\bf{ZF}}, i.e., in Zermelo-Fraenkel set theory without the Axiom of Choice. This article surveys results --- old and new --- that specify how much ``choice'' is needed {\it precisely} to validate each of certain basic analytical and topological results.
Classification : 03E25, 04A25, 26A03, 26A15, 54A35, 54B10, 54C35, 54D20, 54D30, 54D65, 54E45, 54E50, 54E52
Keywords: Axiom of (Countable) Choice; Boolean Prime Ideal Theorem; Theorems of Ascoli; Baire; Čech-Stone and Tychonoff; compact; Lindelöf and orderable spaces 
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     author = {Herrlich, Horst},
     title = {Choice principles in elementary topology and analysis},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {545--552},
     year = {1997},
     volume = {38},
     number = {3},
     mrnumber = {1485074},
     zbl = {0938.54007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1997_38_3_a9/}
}
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Herrlich, Horst. Choice principles in elementary topology and analysis. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 545-552. http://geodesic.mathdoc.fr/item/CMUC_1997_38_3_a9/