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/