On the hyperspace of strictly convex bodies

Author
L. Bazylevych
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
pdf
Table of content of issue