期刊论文详细信息
Commentationes mathematicae Universitatis Carolinae | |
Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum | |
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
【 预 览 】
Files | Size | Format | View |
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RO201904032196911ZK.pdf | 40KB | download |