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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 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.
Abdelhafed Elkhadiri. "The theorem of the complement for a quasi subanalytic set." Studia Mathematica 161.3 (2004): 225-247. <http://eudml.org/doc/284614>.
@article{AbdelhafedElkhadiri2004, abstract = {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.}, author = {Abdelhafed Elkhadiri}, journal = {Studia Mathematica}, keywords = {quasianalytic functions; subanalytic and semianalytic sets; Gabrielov's theorem}, language = {eng}, number = {3}, pages = {225-247}, title = {The theorem of the complement for a quasi subanalytic set}, url = {http://eudml.org/doc/284614}, volume = {161}, year = {2004}, }
TY - JOUR AU - Abdelhafed Elkhadiri TI - The theorem of the complement for a quasi subanalytic set JO - Studia Mathematica PY - 2004 VL - 161 IS - 3 SP - 225 EP - 247 AB - 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. LA - eng KW - quasianalytic functions; subanalytic and semianalytic sets; Gabrielov's theorem UR - http://eudml.org/doc/284614 ER -