Index of a finitistic space and a generalization of the topological central point theorem

In this paper we prove that if $G$ is a p-torus (resp. torus) group acting without fixed points on a finitistic space X (resp. with finitely many orbit types), then the G-index $i_G(X)<1$. Using this G-index we obtain a generalization of the Central Point Theorem and also of the Tverberg Theorem for any d-dimensional Hausdorff space.