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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap3931-7-2016,
author = {Ma\l gorzata Czapla and Wies\l aw Paw\l ucki},
title = {Michael's theorem for Lipschitz cells in o-minimal structures},
journal = {Annales Polonici Mathematici},
volume = {116},
year = {2016},
pages = {101-107},
zbl = {06622309},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3931-7-2016}
}
Małgorzata Czapla; Wiesław Pawłucki. Michael's theorem for Lipschitz cells in o-minimal structures. Annales Polonici Mathematici, Tome 116 (2016) pp. 101-107. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3931-7-2016/