Skip to main content
Log in

Classes of convex sets as generalized metrical spaces

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

The metrization of classes of convex bodies is generalized to a Minkowski space with unsymmetric metric.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. G. C. Shephard and R. J. Webster, “Metrics for sets of convex bodies,” Mathematika,12, No. 1, 73–88 (1965).

    Google Scholar 

  2. G. Ewald, “Van Klassen konvexer Korper erzeugter Hilbert-räume,” Math. Ann.,162, 140–146 (1965).

    Google Scholar 

  3. J. Dieudonné, “Sur la séparation des ensembles convexes,” Math. Ann.,163, 1–3 (1966).

    Google Scholar 

  4. G. Ewald, and G. C. Shephard, “Normed vector spaces consisting of classes of convex sets,” Math. Z.,91, 1–19 (1966).

    Google Scholar 

  5. G. Buzeman, The Geometry of Geodesies [in Russian], Moscow (1962).

  6. I. M. Yaglom and V. G. Boltyanskii, Convex Figures [in Russian], Moscow-Leningrad (1951).

  7. E. A. Zaustinsky, “Spaces with non-symmetric distances,” Mem. Amer. Math. Soc., No. 34 (1959).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 45–52, July, 1968.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sorokin, V.A. Classes of convex sets as generalized metrical spaces. Mathematical Notes of the Academy of Sciences of the USSR 4, 517–521 (1968). https://doi.org/10.1007/BF01429813

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01429813

Keywords

Navigation