2006/04/08 by Theo Buehler, Buehler, Theo
Mathematics · #51F99 #52A30 #Advanced Algebra and Geometry #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Metric Geometry (math.MG) #math.FA #math.MG #msc:51F99 #msc:52A30
paper · pdf · doi:10.48550/arxiv.math/0604187
2 pages, no figures; v2: minor typos fixed
openalex publication_date 2006/04/08 · arxiv created 2007/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use bicombings on arcwise connected metric spaces to give definitions of convex sets and extremal points. These notions coincide with the customary ones in the classes of normed vector spaces and geodesic metric spaces which are convex in the usual sense. A rather straightforward modification of the standard proof of the Krein-Mil'man Theorem yields the result that in a large class of metric spaces every compact convex set is the closed convex hull of its extremal points. The result appears to be new even for CAT(0)-spaces.