---
abstract: 'We prove equivalence of certain axiom sets for affine buildings. Along the lines a purely combinatorial proof of the existence of a spherical building at infinity is given. As a corollary we obtain that “being an affine building” is independent of the metric structure of the space.'
address: 'Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany'
author:
- 'Petra N. Schwer (née Hitzelberger)'
bibliography:
- 'literaturliste.bib'
title: Axioms of affine buildings
---

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[^1]

Introduction {#sec_introduction}
============

Verifying that an object satisfies a certain list of axioms can sometimes be a problem hard to tackle. Once in a while one might wish that there is a shorter equivalent axiom set suited better for the purpose of a given problem. While working on a different project [@BaseChange] we had to verify that a certain space is a generalized affine building in the sense of Bennett [@Bennett]. This was the motivation to prove the main result of the present paper, that is Theorem \[MainThm\].

Adding one axiom to Tits’ list defining non-discrete ${\mathbb{R}}$ buildings, Bennett was able to generalize the concept to arbitrary ordered abelian groups. In [@Bennett] and [@BennettDiss] he defined generalized affine buildings giving a 