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In an Archimedean directed partially ordered vector space , one can define the concept of a band in terms of disjointness. Bands can be studied by using a vector lattice cover  of . If  has an order unit,  can be represented as a subspace of , where  is a compact Hausdorff space. We characterize bands in , and their disjoint complements, in terms of subsets of . We also analyze two methods to extend bands in  to  and show how the carriers of a band and its extensions are related. We use the results to show that in each -dimensional partially ordered vector space with a closed generating cone, the number of bands is bounded by  for . We also construct examples of -dimensional partially ordered vector spaces with  bands. This shows that there are -dimensional partially ordered vector spaces that have more bands than an -dimensional Archimedean vector lattice when .

Bands in partially ordered vector spaces with order unit