A Lefschetz fixed point theorem for multivalued maps of finite spaces

TL;DR

This paper establishes a version of the Lefschetz fixed point theorem tailored for multivalued maps on finite T0 spaces, extending classical fixed point results to a broader class of mappings.

Contribution

It introduces a Lefschetz fixed point theorem specifically for multivalued maps on finite T0 spaces, a novel extension of classical fixed point theory.

Findings

Proves a fixed point theorem for multivalued maps on finite T0 spaces.

Extends classical Lefschetz fixed point theorem to multivalued and finite space contexts.

Provides a new tool for analyzing fixed points in finite topological spaces.

Abstract

We prove a version of the Lefschetz fixed point theorem for multivalued maps $F:X\multimap X$ in which $X$ is a finite $T_0$ space.