Convexities on ordered structures have their Krein--Milman theorem
Functional Analysis
2014-05-30 v3
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.
Cite
@article{arxiv.1301.0760,
title = {Convexities on ordered structures have their Krein--Milman theorem},
author = {Paul Poncet},
journal= {arXiv preprint arXiv:1301.0760},
year = {2014}
}
Comments
34 pages. The final publication is available at http://www.heldermann.de. See http://www.heldermann.de/JCA/JCA21/JCA211/jca21005.htm