Vol. 53, No. 1, 1974

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Strongly unique best approximates to a function on a set, and a finite subset thereof

Martin Bartelt

Vol. 53 (1974), No. 1, 1–9

Let X be a compact Hausdorff space and let C(X) denote the space of continuous real valued functions defined on X, normed by the supremum norm f= maxxX|f(x)|. Let M be a finite dimensional subspace of C(X). This note examines the problem of whether every best (unique best, strongly unique best) approximate to f on X is also a best respectively: unique best, strongly unique best) approximate to f on some finite subset of X. Appropriate converse results are also considered.

Mathematical Subject Classification 2000
Primary: 41A50
Received: 13 July 1973
Revised: 21 September 1973
Published: 1 July 1974
Martin Bartelt