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Chebyshev subspaces of finite codimension in spaces of continuous functions

Published online by Cambridge University Press:  09 April 2009

A. L. Brown
A. L. Brown
Affiliation:
University of Newcastle upon TyneEngland and University of NewcastleNew South Wales, Australia
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Abstract

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A. L. Garkavi in 1967 characterized those compact metric spaces X with the property that the space C(X) of real-valued continuous functions possesses Chebyshev subspaces of fine codimension ≥ 2. Here compact Hausdorif spaces with the same property are characterized in terms of certain standard subspaces of the space [0, 1] × {0, 1} equipped with a lexicographic order topology. Garkavi's result for metric spaces is exhibited as a corollary. The proof depends upon a simplification of a characterization by Garkavi of the Chebyshev subspaces of finite codimension in C(X).

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 41 A 65, 46 E 15; secondary 54 G 99.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 1 , August 1978 , pp. 99 - 109
Copyright
Copyright © Australian Mathematical Society 1978

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