关于非离散仿射建筑的公理化定义
On axiomatic definitions of non-discrete affine buildings
摘要：
在本文中，我们证明了非离散仿射建筑物的公理集的等价性，通过提供不同类型的度量，交换和图集条件。我们应用我们的结果表明，欧几里德建筑物的定义只依赖于模型空间上的度量的拓扑等价类。处理度量条件的公理的尖锐性在附录中说明。证明了定义在度量为d的模型空间上的空间X只有当X上的诱导距离函数满足三角不等式时才可能是建筑物。
英文摘要：
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.
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