A Continuous Mapping That Fixes All Boundary Points but No Interior Points

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Except for the zero shift, each member of this family of continuous mappings of the unit disk into itself fixes the boundary pointwise but has no interior fixed points. (The point is a fixed point of if ) The method used is to map the interior of the disk to the whole plane with , translate by the shift, and map back to the disk with .

Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA




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