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Whitney triangulations of semialgebraic sets

100%

Shiota M.

Annales Polonici Mathematici

2005

tom 87

nr 1

237-246

A compact semialgebraic set admits a semialgebraic triangulation such that the family of open simplexes forms a Whitney stratification and is compatible with a finite number of given semialgebraic subsets.

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Triangulation of subanalytic sets

75%

Shiota M.

Banach Center Publications

1988

tom 20

nr 1

385-395

Clarke critical values of subanalytic Lipschitz continuous functions

51%

Bolte J., Daniilidis A., Lewis A., Shiota M.

Annales Polonici Mathematici

2005

tom 87

nr 1

13-25

The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawłucki's extension of the Puiseux lemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Banach Center Publications

3 Shiota M.

1 Bolte J.

1 Daniilidis A.

1 Lewis A.

2 2005

1 1988

Wyniki wyszukiwania

Whitney triangulations of semialgebraic sets

Triangulation of subanalytic sets

Clarke critical values of subanalytic Lipschitz continuous functions