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Mat. Zametki, 1972, Volume 12, Issue 1, Pages 85–90 (Mi mz9850)  

Covering convex solids by greater homotheties

P. S. Soltan

Kishinev State University

Abstract: Let $K$ be a convex solid of Euclidean space $E^n$, with $\operatorname{bd}K$ and $\operatorname{int}K$ being its boundary and interior. The paper solves the problem of the possibility of covering $K$ by sets homothetic to $\operatorname{int}K$, with the ratio of the homotheties being greater than unity and the centers being in $E^n\setminus\operatorname{int}K$, while, should such a covering exist, an estimate is provided of the least cardinality of the family of sets covering $K$.

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English version:
Mathematical Notes, 1972, 12:1, 483–485

Bibliographic databases:

UDC: 513
Received: 11.01.1971

Citation: P. S. Soltan, “Covering convex solids by greater homotheties”, Mat. Zametki, 12:1 (1972), 85–90; Math. Notes, 12:1 (1972), 483–485

Citation in format AMSBIB
\Bibitem{Sol72}
\by P.~S.~Soltan
\paper Covering convex solids by greater homotheties
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 1
\pages 85--90
\mathnet{http://mi.mathnet.ru/mz9850}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=319057}
\zmath{https://zbmath.org/?q=an:0239.52008}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 1
\pages 483--485
\crossref{https://doi.org/10.1007/BF01094396}


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