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

Martin Bartelt

Vol. 53 (1974), No. 1, 1–9

DOI: 10.2140/pjm.1974.53.1

Abstract

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∥ = max_x∈X|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

Milestones

Received: 13 July 1973

Revised: 21 September 1973

Published: 1 July 1974