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Ak-extreme point is the limit ofk-exposed points

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Abstract

It is proved that the relative boundary of ak-dimensional intersection of a hyperplane and a compact convex body is contained in the closure of the union of all intersections of dimension lower thanp that the same convex body makes with different hyperplanes.

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References

  1. Asplund, E., Sets with unique farthest points (to appear).

  2. Bourbaki, N., 1956, Espaces vectoriels topologiques, chapitre IV. Paris.

  3. Straszewicz, S., 1935, Über exponierte Punkte abgeschlossener Punktmengen,Fund. Math.,24, 139–143.

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Authors and Affiliations

  1. University of California, Berkeley, California

    Edgar Asplund

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  1. Edgar Asplund
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Asplund, E. Ak-extreme point is the limit ofk-exposed points. Israel J. Math. 1, 161–162 (1963). https://doi.org/10.1007/BF02759703

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  • DOI: https://doi.org/10.1007/BF02759703

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