On the ultrametric Stone-Weierstrass theorem and Mahler's expansion

  title={On the ultrametric Stone-Weierstrass theorem and Mahler's expansion},
  author={P. J. Cahen and Jean-Luc Chabert},
  journal={Journal de Theorie des Nombres de Bordeaux},
Nous explicitons une version ultrametrique du theoreme de Stone-Weierstrass. Pour une partie E d'un anneau de valuation V de hauteur 1, nous montrons, sans aucune hypothese sur le corps residuel, que l'ensemble des fonctions polynomiales est dense dans l'anneau des fonctions continues de E dans V si et seulement si la cloture topologique E de E dans le complete V de V est compacte. Nous explicitons ainsi le developpement d'une fonction continue en serie de fonctions polynomiales. 
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© Publications mathématiques de l’I.H.É.S., 1962, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://
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© Mémoires de la S. M. F., 1974, tous droits réservés. L’accès aux archives de la revue « Mémoires de la S. M. F. » (http:// smf.emath.fr/Publications/Memoires/Presentation.html) implique l’accord
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© Bulletin de la S. M. F., 1964, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accord
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