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Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings

100%

Czapla M.

Annales Polonici Mathematici

2010

tom 97

nr 1

1-21

We describe the notion of a weakly Lipschitz mapping on a $C^{q}$ stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.

Michael's theorem for Lipschitz cells in o-minimal structures

63%

Czapla M., Pawłucki W.

Annales Polonici Mathematici

2016

tom 117

nr 2

101-107

A version of Michael's theorem for multivalued mappings definable in o-minimal structures with M-Lipschitz cell values (M a common constant) is proven. Uniform equi-LCⁿ property for such families of cells is checked. An example is given showing that the assumption about the common Lipschitz constant cannot be omitted.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Czapla M.

1 Pawłucki W.

1 2016

1 2010

Wyniki wyszukiwania

Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings

Michael's theorem for Lipschitz cells in o-minimal structures