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Divisible points of compact convex sets

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Abstract

By associating with an affine dependence the resultant of a related probability measure, we are able to define the set ofdivisible points, D(K), of a compact convex setK. Some general properties ofD(K) are discussed, and its equivalence with a set recently introduced by Reay for convex polytopes demonstrated. For polytopes,D(K) is a continuous image of a projective space. A conjecture concerningD(K) is settled affirmatively for cubes.

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Authors and Affiliations

  1. Department of Mathematics, University of Canterbury, Christchurch, New Zealand

    G. R. Wood

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  1. G. R. Wood
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Wood, G.R. Divisible points of compact convex sets. Israel J. Math. 54, 351–365 (1986). https://doi.org/10.1007/BF02764963

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  • DOI: https://doi.org/10.1007/BF02764963

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