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Article
On axiomatic definitions of non-discrete affine buildings
Advances In Geometry
  • Curtis D. Bennett, Loyola Marymount University
  • Petra N. Schwer, University of Muenster
  • Koen Struyve, Ghent University
Document Type
Article - pre-print
Publication Date
7-1-2014
Disciplines
Abstract
In 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.
Publisher Statement

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 Information
Bennett C, Schwer P, Struyve K. On axiomatic definitions of non-discrete affine buildings. Advances In Geometry. July 2014;14(3):381-412.