Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum

Commentationes mathematicae Universitatis Carolinae

Dušan Pokorný¹ 

关键词: convex function;    convex set;    exceptional set;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

We construct a Lipschitz function on $\mathbb R^2$ which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disproves a theorem that appeared in a paper by L.~Pasqualini and was also cited by other authors.

【 授权许可】

CC BY