Given a closed (not necessarly compact) semi-algebraic set in , we construct a non-negative semi-algebraic function such that and such that for sufficiently small, the inclusion of in is a retraction. As a corollary, we obtain several formulas for the Euler characteristic of .
Étant donné un ensemble semi-algébrique fermé (non nécessairement compact) de , nous construisons une fonction semi-algébrique positive et de classe telle que et telle que pour suffisamment petit, l’inclusion de dans soit une rétraction. En corollaire, nous obtenons plusieurs formules pour la caractéristique d’Euler de .
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
@article{AIF_2009__59_1_429_0, author = {Dutertre, Nicolas}, title = {Semi-algebraic neighborhoods of closed~semi-algebraic sets}, journal = {Annales de l'Institut Fourier}, pages = {429--458}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {59}, number = {1}, year = {2009}, doi = {10.5802/aif.2435}, zbl = {1174.14051}, mrnumber = {2514870}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2435/} }
TY - JOUR AU - Dutertre, Nicolas TI - Semi-algebraic neighborhoods of closed semi-algebraic sets JO - Annales de l'Institut Fourier PY - 2009 SP - 429 EP - 458 VL - 59 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2435/ DO - 10.5802/aif.2435 LA - en ID - AIF_2009__59_1_429_0 ER -
%0 Journal Article %A Dutertre, Nicolas %T Semi-algebraic neighborhoods of closed semi-algebraic sets %J Annales de l'Institut Fourier %D 2009 %P 429-458 %V 59 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2435/ %R 10.5802/aif.2435 %G en %F AIF_2009__59_1_429_0
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. http://www.numdam.org/articles/10.5802/aif.2435/
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