Semi-algebraic neighborhoods of closed semi-algebraic sets
نویسنده
چکیده
— Given a closed (not necessarly compact) semi-algebraic set X in Rn, we construct a non-negative semi-algebraic C2 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. Résumé. — Étant donné un ensemble semi-algébrique fermé (non nécessairement compact) X de Rn, nous construisons une fonction semi-algébrique f positive et de classe C2 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.
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