Fixed points for orientation preserving homeomorphisms of the plane which interchange two points

Morton Brown

Vol. 143 (1990), No. 1, 37–41

DOI: 10.2140/pjm.1990.143.37

Abstract

Suppose h is an orientation preserving homeomorphism of the plane which interchanges two points p and q. If A is an arc from p to q, then h has a fixed point in one of the bounded complementary domains of A ∪ h(A).

Mathematical Subject Classification 2000

Primary: 54H25

Milestones

Received: 6 June 1988

Revised: 29 July 1988

Published: 1 May 1990