no. 2
Topological invariants of analytic sets associated with Noetherian families
[Invariants topologiques des ensembles analytiques associés à des familles noethériennes]
Nowel, Aleksandra1
1 Uniwersytet Gdanski, Instytut Matematyki, ul. Wita Stwosza 57, 80-952 Gdansk (POLAND)
Annales de l'Institut Fourier, Tome 55 (2005) no. 2, pp. 549-571.

Soit Ω⊂ℝ n un ensemble semi-analytique compact et soit ℱ une collection de fonctions analytiques réelles définies dans un voisinage de Ω. Soit Y ω le germe en ω∈ω de l’ensemble ⋂ f∈ℱ f -1 (0). Alors il existe des fonctions analytiques v 1 ,v 2 ,...,v s définies dans un voisinage de Ω telles que 1 2χ( lk (ω,Y ω ))=∑ i=1 s sgn v i (ω), pour tout ω∈Ω.

Let Ω⊂ℝ n be a compact semianalytic set and let ℱ be a collection of real analytic functions defined in some neighbourhood of Ω. Let Y ω be the germ at ω of the set ⋂ f∈ℱ f -1 (0). Then there exist analytic functions v 1 ,v 2 ,...,v s defined in a neighbourhood of Ω such that 1 2χ( lk (ω,Y ω ))=∑ i=1 s sgn v i (ω), for all ω∈Ω.

DOI : 10.5802/aif.2107
Classification : 14P15, 32B20
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.

Nowel, Aleksandra 1

1 Uniwersytet Gdanski, Instytut Matematyki, ul. Wita Stwosza 57, 80-952 Gdansk (POLAND) 
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Nowel, Aleksandra. Topological invariants of analytic sets associated with Noetherian families. Annales de l'Institut Fourier, Tome 55 (2005) no. 2, pp. 549-571. doi : 10.5802/aif.2107. https://aif.centre-mersenne.org/articles/10.5802/aif.2107/

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