Semi-algebraic neighborhoods of closed semi-algebraic sets
Annales de l'Institut Fourier, Volume 59 (2009) no. 1, pp. 429-458.

Given a closed (not necessarly compact) semi-algebraic set X in n , we construct a non-negative semi-algebraic 𝒞 2 function f such that X=f -1 (0) and such that for δ>0 sufficiently small, the inclusion of X in f -1 ([0,δ]) is a retraction. As a corollary, we obtain several formulas for the Euler characteristic of X.

Étant donné un ensemble semi-algébrique fermé (non nécessairement compact) X de n , nous construisons une fonction semi-algébrique f positive et de classe 𝒞 2 telle que X=f -1 (0) et telle que pour δ>0 suffisamment petit, l’inclusion de X dans f -1 ([0,δ]) soit une rétraction. En corollaire, nous obtenons plusieurs formules pour la caractéristique d’Euler de X.

DOI: 10.5802/aif.2435
Classification: 14P10, 14P25
Keywords: Tubular neighborhood, semi-algebraic sets, retraction, quasiregular approaching semi-algebraic function, quasiregular approaching semi-algebraic neighborhood
Mot clés : voisinage tubulaire, ensembles semi-algébriques, rétraction, function semi-algébrique approchante quasirégulière, voisinage semi-algébrique approchant quasirégulier
Dutertre, Nicolas 1

1 Université de Provence Centre de Mathématiques et Informatique 39 rue Joliot-Curie 13453 Marseille Cedex 13 (France)
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Dutertre, Nicolas. Semi-algebraic neighborhoods of closed semi-algebraic sets. Annales de l'Institut Fourier, Volume 59 (2009) no. 1, pp. 429-458. doi : 10.5802/aif.2435. https://aif.centre-mersenne.org/articles/10.5802/aif.2435/

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