On weakly $(n-1)$-convex sets in low-dimensional Euclidean spaces

• Date: 2026
• Main Authors: Osipchuk, T., Осіпчук, Тетяна
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2026
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9669
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 514.172 Wе study the properties of generalized convex sets in the real $n$-dimensional Euclidean space $\mathbb{R}^n,$ where $n=2,3,$ known as weakly $(n-1)$-convex sets. An open set in $\mathbb{R}^2$ (respectively, $\mathbb{R}^3$) is called weakly $1$-convex (respectively, weakly $2$-convex) if...