Czasopismo
2000
|
Vol. 48, no 2
|
141--147
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
We prove the following theorem Let S be a polynomially bounded o-minimal structure on (R,+,.) and let f : A --> [R^n] be a continuous, definable function on a compact definable set [A is subset of R^m]. Then there exist a positive real number [alpha belongs to R+] and a definable function C : f(A) --> R+ such that for any x [belongs to] f(A) and any two points p and q in the same connected component of [f^-1](x) there exists a piece-wise analytic curve gamma joinning p and q in [f^-1](x) with length [gamma is less than or equal to C(x)][...]. As a consequence we obtain the regular separation with parameter for definable sets.
Rocznik
Tom
Strony
141--147
Opis fizyczny
Bibliogr. 3 poz.,
Twórcy
autor
- Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland
Bibliografia
- [1] L. van den Dries, C. Miller, Extending Tamm's theorem, Ann. Inst. Fourier (Grenoble), 44 (1994) 1367-1395.
- [2] A. El Khadiri, Borne d'invariant métrigue pour une familie noethérienne, Bull. Pol. Ac.: Math., 46 (1998) 265-275.
- [3] B. Kocel-Cynk, Interior distance of two points in a fiber of a subanalytic map, Bull. Pol. Ac.: Math., this issue, pp. 149-155.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT2-0001-1879