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The theorem of the complement for a quasi subanalytic set

Abdelhafed Elkhadiri (2004)

Studia Mathematica

Let X ⊂ (ℝⁿ,0) be a germ of a set at the origin. We suppose X is described by a subalgebra, Cₙ(M), of the algebra of germs of C functions at the origin (see 2.1). This algebra is quasianalytic. We show that the germ X has almost all the properties of germs of semianalytic sets. Moreover, we study the projections of such germs and prove a version of Gabrielov’s theorem.

The trivial locus of an analytic map germ

H. Hauser, G. Muller (1989)

Annales de l'institut Fourier

We prove: For a local analytic family { X s } s S of analytic space germs there is a largest subspace T in S such that the family is trivial over T . Moreover the reduction of T equals the germ of those points s in S for which X s is isomorphic to the special fibre X 0 .

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