Original Articles

THE RELATIONSHIP BETWEEN LIPSCHITZ EXTENSIONS, BEST APPROXIMATIONS, AND CONTINUOUS SELECTIONS

Published in: Quaestiones Mathematicae
Volume 14 , issue 3 , 1991 , pages: 261–268

DOI: 10.1080/16073606.1991.9631644

Author(s): Sizwe Mabizela The Department of Mathematics,

Keywords: 41A65 , 47H99 , 58C06 , 41A65 , 47H99 , 58C06

Abstract

There is a close relationship that exists between Lipschitz extensions and best approximations. It is shown that for any function that satisfies the Lipschitz condition on a subset of a metric space (X, d) there always exists a best approximation in the subspace

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