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Chebyshev subspaces of finite codimension in spaces of continuous functions
1978
Journal of the Australian Mathematical Society
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 Hausdorff spaces with the same property are characterized in terms of certain standard subspaces of the space [0, 1] x {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
doi:10.1017/s1446788700011575
fatcat:oe5y2nqhbjec7hj45eyogpj5vi