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Sets of constant width in finite dimensional Banach spaces

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Abstract

In Euclidean space a set of constant width has the property that it is not a proper subset of any set of the same diameter. The converse implication is also true. Here we show that if Euclidean is replaced byn-dimensional Banach space the direct statement is true, but the converse statement is false. Attention is drawn to the problem of characterising those Banach spaces of finite dimension for which the converse is true.

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Authors and Affiliations

  1. Bedford College University of London, UK

    H. G. Eggleston

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  1. H. G. Eggleston
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Eggleston, H.G. Sets of constant width in finite dimensional Banach spaces. Israel J. Math. 3, 163–172 (1965). https://doi.org/10.1007/BF02759749

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  • DOI: https://doi.org/10.1007/BF02759749

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