Geodesic
Convexities on Ordered Structures Have Their Krein-Milman Theorem
Journal of convex analysis, Tome 21 (2014) no. 1, pp. 89-12

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22A26, 52A01, 06A06, 06A12, 06B30, 14T05
Mots-clés : Abstract convexity, max-plus convexity, tropical convexity, Krein-Milman theorem, convex geometries, antimatroids, partially ordered sets, semilattices, Lawson semilattices, lattices 
@article{JCA_2014_21_1_JCA_2014_21_1_a4,
     author = {P. Poncet},
     title = {Convexities on {Ordered} {Structures} {Have} {Their} {Krein-Milman} {Theorem}},
     journal = {Journal of convex analysis},
     pages = {89--12},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a4/}
}
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P. Poncet. Convexities on Ordered Structures Have Their Krein-Milman Theorem. Journal of convex analysis, Tome 21 (2014) no. 1, pp. 89-12. http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a4/