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

TL;DR

This paper introduces a G-index for finitistic spaces under p-torus and torus group actions, leading to a generalized Central Point Theorem and Tverberg Theorem applicable to d-dimensional Hausdorff spaces.

Contribution

It establishes a new G-index for finitistic spaces with group actions and generalizes classical theorems to broader topological contexts.

Findings

G-index i_G(X) < 1 for certain group actions

Generalization of the Central Point Theorem

Extension of Tverberg Theorem to d-dimensional Hausdorff spaces

Abstract

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.