A local-global version of the implicit function theorem in o-minimal structures and a generalization of the theorem of Wilkie on covering open sets by open cells are proven.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-2,
author = {Zofia Ambro\.zy and Wies\l aw Paw\l ucki},
title = {On the implicit function theorem in o-minimal structures},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {19-21},
zbl = {06556700},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-2}
}
Zofia Ambroży; Wiesław Pawłucki. On the implicit function theorem in o-minimal structures. Banach Center Publications, Tome 104 (2015) pp. 19-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-2/