On axiomatic definitions of non-discrete affine buildingsAdvances In Geometry
Document TypeArticle - pre-print
AbstractIn this paper we prove equivalence of sets of axioms for non-discrete affine buildings, by providing different types of metric, exchange and atlas conditions. We apply our result to show that the definition of a Euclidean building depends only on the topological equivalence class of the metric on the model space. The sharpness of the axioms dealing with metric conditions is illustrated in an appendix. There it is shown that a space X defined over a model space with metric d is possibly a building only if the induced distance function on X satisfies the triangle inequality.
This is an author-manuscript of an article accepted for publication in Advances In Geometry following peer review. The version of record is available online at: 10.1515/advgeom-2014-0017.
Citation InformationBennett C, Schwer P, Struyve K. On axiomatic definitions of non-discrete affine buildings. Advances In Geometry. July 2014;14(3):381-412.