The Whitney property of a fiber of a definable mapping

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

Abstrakty

EN

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.

Słowa kluczowe

EN

definable sets; o-minimal structure; Whitney property

PL

geometria algebraiczna; o-minimalna struktura; właściwość Whitney'a; zbiór zdefiniowany

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 2
• Strony: 141--147
• Opis fizyczny: Bibliogr. 3 poz.,

Twórcy

autor

Kocel-Cynk B.

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