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

Kocel-Cynk B.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 2

149-155

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.