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Results in Mathematics

, Volume 41, Issue 3–4, pp 346–360 | Cite as

The Metric Completion of Convex Sets and Modules

  • Dieter Pumplün
Article

Abstract

A convex module is a set closed under convex combinations but not necessarily a subset of a linear space. Convex modules are a natural generalization of convex sets in linear spaces. Any-convex module has a canonical semimetric and there is a universal affine mapping into a convex set, complete in this metric. This completion is the base of a base normed Banach space.

AMS subject classification

52 A 05 52 A 01 46 B 40 46 A 55 

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • Dieter Pumplün
    • 1
  1. 1.Fachbereich MathematikFernUniversitätHagenGermany

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