Choice principles in elementary topology and analysis

Horst Herrlich

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 3, page 545-552
  • ISSN: 0010-2628

Abstract

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Many fundamental mathematical results fail in 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 precisely to validate each of certain basic analytical and topological results.

How to cite

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Herrlich, Horst. "Choice principles in elementary topology and analysis." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 545-552. <http://eudml.org/doc/248085>.

@article{Herrlich1997,
abstract = {Many fundamental mathematical results fail in 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 precisely to validate each of certain basic analytical and topological results.},
author = {Herrlich, Horst},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Axiom of (Countable) Choice; Boolean Prime Ideal Theorem; Theorems of Ascoli; Baire; Čech-Stone and Tychonoff; compact; Lindelöf and orderable spaces; axiom of choice; Zermelo-Fraenkel set theory; compact space; Lindelöf space; orderable space},
language = {eng},
number = {3},
pages = {545-552},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Choice principles in elementary topology and analysis},
url = {http://eudml.org/doc/248085},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Herrlich, Horst
TI - Choice principles in elementary topology and analysis
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 545
EP - 552
AB - Many fundamental mathematical results fail in 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 precisely to validate each of certain basic analytical and topological results.
LA - eng
KW - Axiom of (Countable) Choice; Boolean Prime Ideal Theorem; Theorems of Ascoli; Baire; Čech-Stone and Tychonoff; compact; Lindelöf and orderable spaces; axiom of choice; Zermelo-Fraenkel set theory; compact space; Lindelöf space; orderable space
UR - http://eudml.org/doc/248085
ER -

References

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