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Currently displaying 1 – 2 of 2

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

Małgorzata Czapla — 2010

Annales Polonici Mathematici

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

Małgorzata Czapla; Wiesław Pawłucki — 2016

Annales Polonici Mathematici

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.

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