A topological central point theorem

TL;DR

This paper extends the topological central point theorem and Tverberg theorem to maps from a simplex into finite-dimensional metric spaces, broadening their applicability in topological combinatorics.

Contribution

It provides a generalized version of the topological central point theorem and Tverberg theorem for finite-dimensional metric spaces.

Findings

Established a generalized topological central point theorem.

Extended Tverberg theorem to new classes of spaces.

Demonstrated applications in topological combinatorics.

Abstract

In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.