## 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

Zbl 0494.55001
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