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Fixed points for orientation preserving homeomorphisms of the plane which interchange two points. (English) Zbl 0728.55001

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.

MSC:

55M20 Fixed points and coincidences in algebraic topology

Citations:

Zbl 0494.55001
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