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THÉORIE DES ENSEMBLES. — Une forme abstraite du théorème de Borel-Lebesgue généralisé

In: Selecta Mathematica

Author

Listed:
  • M. Karl Menger
  • M. Élie Cartan

Abstract

Résumé Le théorème de Borel-Lebesgue généralisé énonce Péquivalence des deux propriétés suivantes d’un espace E : I° Pour chaque sous-ensemble E′ de E, toute famille F′ de sous-ensembles de E qui couvre E′ contient une famille dénombrable qui couvre E′. (On dit que la famille F′ couvre E′ si pour chaque point p de E′ la famille F′ contient au moins un ensemble contenant p dans son intérieur.) 2° Chaque sous-ensemble non dénombrable E′ de E contient au moins un point p tel que tout ensemble dont p est un point intérieur contient dans son intérieur un sous-ensemble non dénombrable de E′.

Suggested Citation

  • M. Karl Menger & M. Élie Cartan, 2002. "THÉORIE DES ENSEMBLES. — Une forme abstraite du théorème de Borel-Lebesgue généralisé," Springer Books, in: Bert Schweizer & Abe Sklar & Karl Sigmund & Peter Gruber & Edmund Hlawka & Ludwig Reich & Leopold Sc (ed.), Selecta Mathematica, pages 215-217, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-6110-4_17
    DOI: 10.1007/978-3-7091-6110-4_17
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