We characterise the set on which an infinitely differentiable function can be locally polynomial.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-2-5, author = {T. W. K\"orner}, title = {Smooth Cantor functions}, journal = {Colloquium Mathematicae}, volume = {107}, year = {2007}, pages = {231-238}, zbl = {1125.26006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-2-5} }
T. W. Körner. Smooth Cantor functions. Colloquium Mathematicae, Tome 107 (2007) pp. 231-238. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-2-5/