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Discrete & Computational Geometry

, Volume 15, Issue 1, pp 63–71 | Cite as

Star-shaped sets in normed spaces

  • V. Boltyanski
  • H. Martini
  • P. S. Soltan
Article
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Abstract

We prove a generalization of the Krasnosel’ski theorem on star-shaped sets. Usingd-segments inn-dimensional Minkowski spaces instead of usual segments, the notions “d-visibility” and “d-star-shapedness” are introduced. Our main aim is to give necessary and sufficient conditions ford-star-shapedness in finite-dimensional normed spaces.

Keywords

Minkowski Space Discrete Comput Geom Nonempty Intersection Minkowski Plane Linear Sense 
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Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • V. Boltyanski
    • 1
  • H. Martini
    • 2
  • P. S. Soltan
    • 3
  1. 1.MoscowRussia
  2. 2.Fakultät für MathematikTU Chemnitz-ZwickauChemnitzGermany
  3. 3.KishinevRepublica Moldova

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