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Journal Articles Journal of Convex Analysis Year : 2014

Convexities on ordered structures have their Krein--Milman theorem

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.

Dates and versions

hal-00922374 , version 1 (26-12-2013)

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