  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.
