A Short Proof of the Cartwright-Littlewood Fixed Point Theorem

Abstract

The purpose of this paper is to give a short proof of the Cartwright-Littlewood fixed point theorem (2, p. 3, Theorem A).Theorem A. If T is a (1-1) continuous and orientation preserving transformation of the Euclidean plane E onto itself which leaves a bounded continuum M invariant and if M does not separate E, then some point of M is left fixed by T.