Interior distance of two points in a fiber of a subanalytic map

• Autorzy: Kocel-Cynk, B.
• Języki publikacji: EN

Abstrakty

EN

The aim of the paper is to prove the following theorem: Let N and M be two analytic manifolds and let K [is subset of] N be a compact subanalytic subset. For any continuous subanalytic map f : K --> M there exists a constant C > 0 such that for any y [belongs to] f(K) and any two points p, q in the same connected component of the fiber [f^-1](y) there exists a subanaiytic curve joining p and q in [f^-1](y) of length less than C.

Słowa kluczowe

PL

o-minimalna struktura; odwzorowanie subanalityczne; zbiór subanalityczny

EN

cell decomposition; o-minimal structure; subanalytic map; subanalytic set

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 2
• Strony: 149--155
• Opis fizyczny: Bibliogr. 9 poz.,

Twórcy

autor

Kocel-Cynk, B.

• Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland

Bibliografia

• [1] Z. Denkowska, S. Łojasiewicz, J. Stasica, Sur le nombre des composantes connexes de la section d'un sous-analytique, Bull. Ac. Pol.: Math., 30 (1982) 333-335.
• [2] Z. Denkowska, K. Kurdyka, Une propriéte métrique des fibres d'un sous-analytique, C. R. Acad. Sci. Paris Sr. I Math., 299 (1985) 799-801.
• [3] L. van den Dries, A generalization of the Tarski-Seidenberg theorem, and some nondefinabolity results, Bull. Amer. Math. Soc., 15 (1986) 189-193.
• [4] L. van den Dries, C. Miller, Extending Tamm 's theorem, Ann. Inst. Fourier (Grenoble), 44 (1994) 1367-1395.
• [5] A. El Khadiri, Borne d'invariant métrigue pour une familie noethérienne, Bull. Pol. Ac.: Math., 46 (1998) 265-275. .
• [6] R. M. Hardt, Some analytics bounds for subanalytic sets, in: Differential-geometric control theory, Progr. Math., Birkhaüser, Boston 1983, 259-267.
• [7] S. Łojasiewicz Stratifications et triangulations sous-analytiques, in: Geometry Seminars 1986, Univ. Stud. Bologna, Bologna 1986, 83-89.
• [8] B. Teissier, Sur trois questions de finitude en géometrie analytique, Appendix to a paper by F. Trève, Acta Math., 151 (1983) 1-38.
• [9] Y. Yomdin, Metric properties of semi-algebraic sets and mappings and their applications in smooth analysis, Proc. Larabida Conf., Hermann (1985).