Fixed-point free maps of Euclidean spaces
Volume 212 / 2011
Fundamenta Mathematicae 212 (2011), 1-16
MSC: 54H25, 58C30.
DOI: 10.4064/fm212-1-1
Abstract
Our main result states that every fixed-point free continuous self-map of ${\mathbb R}^{n}$ is colorable. This result can be reformulated 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
