It is proved that the set of smooth points of a semialgebraic set is semialgebraic.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-2-5, author = {Jacek Stasica}, title = {Smooth points of a semialgebraic set}, journal = {Annales Polonici Mathematici}, volume = {81}, year = {2003}, pages = {149-153}, zbl = {1056.14080}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-2-5} }
Jacek Stasica. Smooth points of a semialgebraic set. Annales Polonici Mathematici, Tome 81 (2003) pp. 149-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-2-5/