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Convexity of Chebyshev Sets

  • Frank Deutsch
Chapter
Part of the CMS Books in Mathematics / Ouvrages de mathématiques de la SMC book series (CMSBM)

Abstract

In Theorem 3.5 we saw that every closed convex subset of a Hilbert space is a Chebyshev set. In this chapter we will study the converse problem of whether or not every Chebyshev subset of a Hilbert space must be convex.

Keywords

Hilbert Space Product Space Normed Linear Space Smooth Banach Space Smooth Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • Frank Deutsch
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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