# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## The theorem of the complement for a quasi subanalytic set

### Tom 161 / 2004

Studia Mathematica 161 (2004), 225-247 MSC: Primary 32Bxx, 14Pxx; Secondary 26E10. DOI: 10.4064/sm161-3-2

#### Streszczenie

Let $X\subset ({\mathbb R}^n,0)$ be a germ of a set at the origin. We suppose $X$ is described by a subalgebra, $C_n(M)$, of the algebra of germs of $C^{\infty }$ 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.