Fixed-point free maps of Euclidean spaces

Details Fixed-point free maps of Euclidean spaces Fixed-point free maps of Euclidean spaces

2010-11-23

arxiv.org/abs/1011.4990v1

Mathematics

General Topology

Scientific paper

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 $f: {\mathbb R}^{n}\to {\mathbb R}^{n}$ is fixed-point free iff
$\widetilde f: \beta {\mathbb R}^{n}\to \beta {\mathbb R}^{n}$ is fixed-point
free. We also obtain a generalization of this fact and present some examples.

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