Abstract

We show analogues of the classical Krein-Milman theorem for several ordered algebraic structures, especially in a semilattice (non-linear) framework. In that case, subsemilattices are seen as convex subsets, and for our proofs we use arguments from continuous lattice theory and abstract convexity theory.

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Keywords

  • Abstract convexity
  • max-plus convexity
  • tropical convexity
  • Krein-Milman theorem
  • convex geometries
  • antimatroids
  • partially ordered sets
  • semilattices
  • Lawson semilattices
  • lattices

Mathematics Subject Classification

22A26; 52A01, 06A06, 06A12, 06B30, 14T05

Suggested citation

P. Poncet. “Convexities on Ordered Structures Have Their Krein-Milman Theorem.” Journal of Convex Analysis 21 (2014), No. 1, 89–120.

Copyright Heldermann Verlag 2014