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Coverings by convex bodies and inscribed balls |
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| Authors: | Vladimir Kadets |
| Affiliation: | Department of Mechanics and Mathematics, Kharkov National University, pl. Svobody 4, 61077 Kharkov, Ukraine |
| Abstract: | Let  be a Hilbert space. For a closed convex body  denote by  the supremum of the radiuses of balls contained in  . We prove that  for every covering of a convex closed body  by a sequence of convex closed bodies  ,  . It looks like this fact is new even for triangles in a 2-dimensional space. |
| Keywords: | Hilbert space convex sets inscribed ball |
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