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Fonctions Régulues
Goulwen Fichou1, Johannes Huisman2, Frédéric Mangolte3, Jean-Philippe Monnier3

We study the ring of rational functions admitting a continuous extension to the real affine space. We establish several properties of this ring. In particular, we prove a strong Nullstelensatz. We study the scheme theoretic properties and prove regulous versions of Theorems A and B of Cartan. We also give a geometrical characterization of prime ideals of this ring in terms of their zero-locus and relate them to euclidean closed Zariski-constructible sets.
1:  IRMAR - Institut de Recherche Mathématique de Rennes
2:  LM - Laboratoire de mathématiques de Brest
3:  LAREMA - Laboratoire Angevin de REcherche en MAthématiques
Géométrie algébrique réelle