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On the Complexity of 2D Discrete Fixed Point Problem
Complexity 2D Discrete Fixed Point Problem
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2012/12/3
While the 3-dimensional analogue of Sperner’s problem in the plane was known to be complete in class PPAD, the complexity of 2D-SPERNER itself is not known to be PPAD-complete or not. In this paper, w...
Fixed-point free maps of Euclidean spaces
Fixed-point Euclidean spaces
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2010/11/24
Our main result states that every fixed-point free continuous self-map of ${\mathbb R}^{n}$ is colorable. This result can be re-formulated as follows: A continuous map $f: {\mathbb R}^{n}\to {\mathbb...