Geometric structure and classification of infinite-dimensional halfspaces

Abstract

Using an analytical representation of finite-dimensional halfspaces with aid of linear operators and lexicographical orders J.-E. Martinez–Legaz and I. Singer have classified halfspaces of a finite-dimensional vector space by types and ranks. In the paper we extend their classification to infinite-dimensional halfspaces. Our approach to classification is based on order and geometric characterizations of halfspaces rather than any analytical representations of ones.