| Title | On weakly m-convex sets |
| Publication Type | Journal Article |
| Year of Publication | 2017 |
| Authors | Dakhil, HK, Zelinskii, Yu.B, Klishchuk, BA |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2017.04.003 |
| Issue | 4 |
| Section | Mathematics |
| Pagination | 3-6 |
| Date Published | 4/2017 |
| Language | Ukrainian |
| Abstract | Some properties of weakly m-convex sets are studied. Various variants of the problem of shadow are investigated. The lower bound for the number of balls that are necessary to create a shadow at a point tangential to sphere $S^{2}$ in the Euclidean space $\mathbb{R}^{3}$, is obtained.
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| Keywords | 1-hull of a family of sets, conjugate set, Grassmann manifold, m-convex set, problem of shadow, weakly m-convex set |
References:
- Zelinskii, Yu. B. (2012). Convexity. Selected topics. Kiev: Institute of Mathematics of the NAS of Ukraine (in Russian).
- Zelinskii, Yu. B., Momot, I. V. (2001). On the (n, m) convex sets. Ukr. Math. J., 53, No 3, rpp. 422-427 (in Russian). https://doi.org/10.1023/A:1012352607365
- Zelinskii, Yu. B., Gretsky, A. S., Momot, I. V. Some results on generalized convex sets. Classical analysis, Proceedings of 10-th intern. sympos. Poland, 1999, pp. 113-124.
- Rohlin, V. A., Fuks, D. B. (1977). Basic Topology Course. Moscow: Nauka (in Russian).
- Zelinskii, Yu. B. (2015). The problem of shadow for family of sets. Zbirnyk prats' In-tu matematyky NAN Ukrainy, 12, No 4: 197-204 (in Russian).
