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/