Three Brouwer fixed point theorems for homeomorphisms of the plane

TL;DR

This paper revisits and proves three classical fixed point theorems for orientation-preserving homeomorphisms of the plane, based on Brouwer's earlier, lesser-known results.

Contribution

It provides new proofs of three Brouwer fixed point theorems for plane homeomorphisms, clarifying and restoring historical results.

Findings

Established existence of fixed points for certain plane homeomorphisms

Reconnected modern results with Brouwer's original theorems

Enhanced understanding of fixed point properties in plane topology

Abstract

We prove three theorems giving fixed points for orientation preserving homeomorphisms of the plane following forgotten results of Brouwer.