Vol. 59, No. 1, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Fixed points for orientation preserving homeomorphisms of the plane which interchange two points

Emilio Gagliardo and Clifford Alfons Kottman

Vol. 59 (1975), No. 1, 27–32

Let T be an orientation preserving homeomorphism defined on a subset of the plane which interchanges two points, P and Q. Let Γ be a simple curve joining P and Q and let Ω be a simply connected set contained in the domain and range of T such that Γ Ω,T(Γ) Ω,T1(Γ) Ω. Then T has a fixed point in Ω. A corollary concerning fixed points of homeomorphisms on S2 follows.

The proof would be trivial if T were necessarily an element of a flow on the plane, however an example given in this paper shows that this need not be the case.

Mathematical Subject Classification 2000
Primary: 54H25
Received: 31 July 1974
Revised: 28 April 1975
Published: 1 July 1975
Emilio Gagliardo
Clifford Alfons Kottman