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Convexities on ordered structures have their Krein--Milman theorem

Paul Poncet 1, 2 
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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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Submitted on : Thursday, December 26, 2013 - 11:58:25 AM
Last modification on : Thursday, January 20, 2022 - 5:26:32 PM

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  • HAL Id : hal-00922374, version 1
  • ARXIV : 1301.0760



Paul Poncet. Convexities on ordered structures have their Krein--Milman theorem. Journal of Convex Analysis, Heldermann, 2014, 21 (1), pp.89--120. ⟨hal-00922374⟩



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