Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T12:13:53.548Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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