Let be a compact semianalytic set and let be a collection of real analytic functions defined in some neighbourhood of . Let be the germ at of the set . Then there exist analytic functions defined in a neighbourhood of such that , for all .
Soit un ensemble semi-analytique compact et soit une collection de fonctions analytiques réelles définies dans un voisinage de . Soit le germe en de l’ensemble . Alors il existe des fonctions analytiques définies dans un voisinage de telles que , pour tout .
Keywords: germs of semianalytic sets, Noetherian families, (sum of signs of) analytic functions, $\Omega $-Noetherian algebra
Mot clés : germes d’ensembles semi-analytiques, familles noethériennes, (somme des signes de) fonctions analytiques, algèbre $\Omega $-noethérienne.
@article{AIF_2005__55_2_549_0, author = {Nowel, Aleksandra}, title = {Topological invariants of analytic sets associated with {Noetherian} families}, journal = {Annales de l'Institut Fourier}, pages = {549--571}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {2}, year = {2005}, doi = {10.5802/aif.2107}, mrnumber = {2147900}, zbl = {1072.14073}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2107/} }
TY - JOUR AU - Nowel, Aleksandra TI - Topological invariants of analytic sets associated with Noetherian families JO - Annales de l'Institut Fourier PY - 2005 SP - 549 EP - 571 VL - 55 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2107/ DO - 10.5802/aif.2107 LA - en ID - AIF_2005__55_2_549_0 ER -
%0 Journal Article %A Nowel, Aleksandra %T Topological invariants of analytic sets associated with Noetherian families %J Annales de l'Institut Fourier %D 2005 %P 549-571 %V 55 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2107/ %R 10.5802/aif.2107 %G en %F AIF_2005__55_2_549_0
Nowel, Aleksandra. Topological invariants of analytic sets associated with Noetherian families. Annales de l'Institut Fourier, Volume 55 (2005) no. 2, pp. 549-571. doi : 10.5802/aif.2107. http://archive.numdam.org/articles/10.5802/aif.2107/
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