Article
MSC:
03E25,
04A25,
26A03,
26A15,
54A35,
54B10,
54C35,
54D20,
54D30,
54D65,
54E45,
54E50,
54E52 | MR 1485074 | Zbl 0938.54007
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Keywords:
Axiom of (Countable) Choice; Boolean Prime Ideal Theorem; Theorems of Ascoli; Baire; Čech-Stone and Tychonoff; compact; Lindelöf and orderable spaces
Axiom of (Countable) Choice; Boolean Prime Ideal Theorem; Theorems of Ascoli; Baire; Čech-Stone and Tychonoff; compact; Lindelöf and orderable spaces
Summary:
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.
References:
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