The modulus of continuity of the operator of best approximation on a subspace tends towards zero uniformly on the class of all subspaces of an n-dimensional space only if the unit ball of the space contains no extremal subsets of dimensionality k (0 < k < n-1).
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Translated from Matematicheskie Zametki, Vol. 16, No. 3, pp. 501–511, September, 1974.
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Berdyshev, V.I. Operator of best approximation on finite-dimensional subspaces. Mathematical Notes of the Academy of Sciences of the USSR 16, 888–893 (1974). https://doi.org/10.1007/BF01148141
- Unit Ball
- Extremal Subset