Skip to main content
SpringerLink
Log in

Convexity of Chebyshev sets

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Busemann, H.: Note on a theorem of convex sets. Mat. Tidsskr. B. 1947, 32–34.

  2. Day, M. M.: Normed linear spaces. Ergeb. Math. Grenz. no. 21. Berlin 1959.

  3. Eflmov, N. V., andS. B. Stechkin: Chebyshev sets in Banach spaces (Russian). Doklady Akad. Nauk SSSR121, 582–585 (1958).

    Google Scholar 

  4. Efimov, N. V., andS. B. Stechkin: Some supporting properties of sets in Banach spaces as related to Chebyshev sets (Russian). Doklady Akad. Nauk SSSR127, 254–257 (1959).

    Google Scholar 

  5. Fan, Ky, andI. Glicksberg: Some geometric properties of the spheres in a normed linear space. Duke Math. J.25, 553–568 (1958).

    Google Scholar 

  6. James, R. C.: Reflexivity and the supremum of linear functionals. Ann. Math.66, 159–169 (1957).

    Google Scholar 

  7. Jessen, B.: Two theorems on convex point sets (Danish). Mat. Tidsskr. B. 1940, 66–70.

  8. Kalisch, G. K., andE. G. Straus: On the determination of points in a Banach space by their distances from the points of a given set. An. Acad. Brasil Ci.29, 501–519 (1957).

    Google Scholar 

  9. Klee, V.: Convex bodies and periodic homeomorphisms in Hilbert space. Trans. Am. Math. Soc.74, 10–43 (1953).

    Google Scholar 

  10. Klee, V.: Relative extreme points and weak compactness. Proceedings of the International Symposium on Linear Spaces. Jerusalem, July 1960.

  11. Mazur, S.: Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält. Studia Math.2, 7–9 (1930).

    Google Scholar 

  12. Motzkin, Th.: Sur quelques propriétés caractéristiques des ensembles convexes. Atti. R. Accad. Lincei, Rend. VI s. 21, 562–567 (1935).

    Google Scholar 

  13. Motzkin, T. S., E. G. Straus andF. A. Valentine: The number of farthest points. Pacific J. Math.3, 221–232 (1953).

    Google Scholar 

  14. Ruston, A. F.: A note on convexity in Banach spaces. Proc. Cambridge Philos. Soc.45, 157–159 (1949).

    Google Scholar 

  15. Tychonov, A.: Ein Fixpunktsatz. Math. Ann.111, 767–776 (1935).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Seattle and Copenhagen

    Victor Klee

Authors
  1. Victor Klee
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research fellow of the Alfred P. Sloan Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klee, V. Convexity of Chebyshev sets. Math. Ann. 142, 292–304 (1961). https://doi.org/10.1007/BF01353420

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01353420

Search

Navigation