On a Topological Generalization of a Theorem of Tverberg

Let Aj denote the./-dimensional simplex. The support of the point x e Aj is the minimal face of Aj containing x. A face of Aj is understood to be closed. The well-known theorem of Radon 3 can be formulated as follows. PROPOSITION 1. For any linear map f: An + 1- R there exist two disjoint faces A