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A fixed-point anomaly in the plane

Charles L. Hagopian, Janusz R. Prajs (2005)

Fundamenta Mathematicae

We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ D does not have the fixed-point property. This example answers a question of R. H. Bing. The continuum M is a countable union of arcs.

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