Abstract
We establish characteristic properties of a subspace L of finite codimension of the space C(T) that has a Chebyshev center and a Chebyshev net for every compact set from C(T). We show that these properties are the same as the conditions for the existence in L of an element of best approximation for every element from C(T).
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Literature cited
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Additional information
Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 469–478, October, 1973.
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Garkavi, A.L. The conditional Chebyshev center of a compact set of continuous functions. Mathematical Notes of the Academy of Sciences of the USSR 14, 827–831 (1973). https://doi.org/10.1007/BF01108806
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DOI: https://doi.org/10.1007/BF01108806