Abstract
The present paper characterizes the topological structure of real traces. This is done in terms of graph-theoretic properties of the underlying (possibly infinite) dependence alphabet. The topological space of real traces is shown to be homeomorphic to the direct product of (at most) the full binary tree and the full countably branching tree and one higher-dimensional grid. The occurrence of each of these factors depends on the existence of finite non-trivial and of infinite connected components and on the number of isolated letters of the dependence alphabet.
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