| Title | Extremal elements in a hypercomplex space |
| Publication Type | Journal Article |
| Year of Publication | 2016 |
| Authors | Stefanchuk, MV |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2016.04.013 |
| Issue | 4 |
| Section | Mathematics |
| Pagination | 13-19 |
| Date Published | 4/2016 |
| Language | Ukrainian |
| Abstract | Extremal elements and a $h$-hull of sets in the $n$-dimensional hypercomplex space $\mathbb{H}^{n}$ are investigated. The class of $\mathbb{H}$-quasiconvex sets including strongly hypercomplex convex sets and being closed with respect to intersections is introduced.
|
| Keywords | h-extremal beam, h-extremal point, h-hull of a set, H-quasiconvex set, hypercomplex convex set, strongly hypercomplex convex set |
References:
- Zelinskii Yu. B. Convexity. Selected chapters, Kyiv: Institute of Mathematics of the NAS of Ukraine, 2012 (in Russian).
- Kantor I. L., Solodovnikov A. S. Hypercomplex numbers, Moscow: Nauka, 1973 (in Russian).
- Mkrtchyan G. A. On hypercomplex convex sets, Preprint, AS USSR, Institute of Mathematics, 87.42, Kyiv, 1987 (in Russian).
- Mkrtchyan G. A. On hypercomplex convexity, V Tiraspol. workshop on general topology, Kishinev: Shtiintsa, 1985 (in Russian).
- Mkrtchyan G. A. Ukr. Mat. J., 1990, 42, No 2: 182–187 (in Russian).
- Zelinskii Yu. B., Mkrtchyan G. A. Dokl. AN SSSR, 1990, 311, No 6: 1299–1302 (in Russian).
- Leyhtveys K. Convex sets, Moscow: Nauka, 1985 (in Russian).
- Spener E. Algebraic topology, Moscow: Mir, 1971 (in Russian).
