The horofunction boundary of finite-dimensional normed spaces
Abstract
Description
We determine the set of Busemann points of an arbitrary finite-dimensional normed space. These are the points of the horofunction boundary that are the limits of "almost-geodesics". We prove that all points in the horofunction boundary are Busemann points if and only if the set of extreme sets of the dual unit ball is closed in the Painleve-Kuratowski topology.
11 pages v2. Some proofs streamlined and another example added
11 pages v2. Some proofs streamlined and another example added