The sufficient conditions are obtained for the existence, on a hyper surface M ⊂ Rn, of k points whose convex hull forms a (k-1)-dimensional simplex, homothetic to a given simplex Δ ⊂ Rn. In particular, it is shown that if M is a smooth hypersurface, homeomorphic to a sphere, such points will exist for any simplex Δ ⊂ Rn. The proofs are based on simple topological considerations. There are six references.
|Original language||English (US)|
|Number of pages||5|
|Journal||Mathematical Notes of the Academy of Sciences of the USSR|
|State||Published - Jan 1969|
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