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L'axiome de normalité pour les espaces totalement ordonnés

Published online by Cambridge University Press:  12 March 2014

Labib Haddad  and
Marianne Morillon
Labib Haddad
Affiliation:
120 Rue de Charonne, 75011 Paris, France
Marianne Morillon
Affiliation:
33 Rue de Bizaleix, 63500 Issoire, France
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Abstract

We show that the following property (LN) holds in the basic Cohen model as sketched by Jech: The order topology of any linearly ordered set is normal. This proves the independence of the axiom of choice from LN in ZF, and thus settles a question raised by G. Birkhoff (1940) which was partly answered by van Douwen (1985).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 1 , March 1990 , pp. 277 - 283
Copyright
Copyright © Association for Symbolic Logic 1990

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References

RÉFÉRENCES

[1]Birkhoff, G., Lattice theory, 3rd ed., American Mathematical Society, Providence, Rhode Island, 1967; corrected reprint, 1979.Google Scholar
[2]van Douwen, E. K., Horrors of topology without AC: a nonnormal orderable space, Proceedings of the American Mathematical Society, vol. 95 (1985), pp. 101–105.Google Scholar
[3]Jech, T. J., The axiom of choice, North-Holland, Amsterdam, 1973.Google Scholar
[4]Morillon, M., Topologie, analyse nonstandard et axiome du choix, Thèse de troisième cycle, Université Blaise Pascal (Clermont II), Clermont-Ferrand, 1988.Google Scholar
[5]Morillon, M., Ensembles totalement ordonnés et axiome de choix, Seminaire d'Analyse 1987/88, Université Blaise Pascal (Clermont II) (a paraitre).Google Scholar