We describe the notion of a weakly Lipschitz mapping on a 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap97-1-1, author = {Ma\l gorzata Czapla}, title = {Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings}, journal = {Annales Polonici Mathematici}, volume = {98}, year = {2010}, pages = {1-21}, zbl = {1183.14072}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap97-1-1} }
Małgorzata Czapla. Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings. Annales Polonici Mathematici, Tome 98 (2010) pp. 1-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap97-1-1/