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@David Here are the citations from those papers: K. Borsuk, On the imbedding of systems of compacta in simplicial complexes , Fund. Math 35, (1948) 217-234 J. Leray. Sur la forme des espaces topologiques et sur les points fixes des représentations. J. Math. Pures Appl. 24:95–167, 1945 But it is not clear that these are the first instances of such a result. @Benjamin: I refer to the version which holds for contractible nerves in a paracompact space.
As much as I adore the arXiv, it is downright silly to start hunting for online preprints of each paper you are reviewing. And what's worse, often the arXiv version is not the same as the draft that reaches you.
