## Proceedings of the Centre for Mathematics and its Applications

### An approximation theoretic characterisation of inner product spaces

A. L. Brown

#### Abstract

Two approximation theoretic properties of Hilbert spaces used in the proof of a result concerning Chebyshev sets obtained by Frerking and Westphal [4] are discussed. Investigation of one leads to a characterisation of inner product spaces of dimension at least three; it is an improvement of one due to Berens [3]. The other property is shared by all finite dimensional spaces [3] and here a topological result of which that fact is a simple consequence is proved.

#### Article information

Dates
First available in Project Euclid: 18 November 2014