Brown, Morton Fixed points for orientation preserving homeomorphisms of the plane which interchange two points. (English) Zbl 0728.55001 Pac. J. Math. 143, No. 1, 37-41 (1990). In this note the author proves: “Let h be an orientation preserving homeomorphism of the plane which interchanges two points p and q. If A is an arc from p to q where f has no fixed points in A, then h has a fixed point in one of the bounded complementary domains of \(A\cup h(A)''\). The proof uses simple properties of the winding number and that the set consisting of \(A\cup h(A)\) and the union with its bounded complementary domains is contractible. Reviewer: D.Gonçalves (São Paulo) Cited in 1 ReviewCited in 5 Documents MSC: 55M20 Fixed points and coincidences in algebraic topology Keywords:index; orientation preserving homeomorphism; plane; winding number Citations:Zbl 0494.55001 PDF BibTeX XML Cite \textit{M. Brown}, Pac. J. Math. 143, No. 1, 37--41 (1990; Zbl 0728.55001) Full Text: DOI OpenURL