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

@article{Cahen2002OnTU,
  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},
  year={2002},
  volume={14},
  pages={43-57}
}
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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