On the hyperspace of strictly convex bodies |
|
| Author |
Institute of Applied Problems in Mechanics and Mathematics, Naukova 3b,
Lviv, 290601, Ukraine
|
| Abstract |
It is proved that the subset of smooth strictly convex bodies forms a pseudointerior
in the hyperspace of compact convex subsets of the unit cube of Euclidean space.
|
| Keywords |
smooth strictly convex bodies, pseudointerior, hyperspace, compact convex subsets, unit cube, Euclidean space
|
| DOI |
doi:10.30970/ms.2.1.83-86
|
Reference |
1. Zamfirescu T. Nearly all convex bodies are smooth and strictly convex // Monatsh. Math. 1987. Bd.103, N.1. S.57–62.
2. Zamfirescu T. Too long shadow boundaries // Proc. Amer. Math. Soc. 1988. V.103, N.2. P.587–590. 3. Klee V. Some new results on smoothness and rotundity in normed linear spaces // Math. Ann. 1959. Bd.139, N.1. S.51–63. 4. Nadler S.B., Quinn J.E., Stavrakas N.M. Hyperspaces of compact convex sets // Bull. Acad. Polon. Sci. Ser. Math. 1977. V.25, N.4. P.381–385. 5. Bessaga C., Pelczynski A. Selected topics in infinite-dimensional topology.– Warszawa: PWN, 1975. Institute of Applied Problems in Mechanics and Mathematics, Naukova 3b, Lviv, 290601, Ukraine |
| Pages |
83-86
|
| Volume |
2
|
| Issue |
1
|
| Year |
1993
|
| Journal |
Matematychni Studii
|
| Full text of paper | |
| Table of content of issue |