  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.
