Fixed-point free maps of Euclidean spaces

R. Z. Buzyakova¹ ; A. Chigogidze¹

¹ Department of Mathematics and Statistics The University of North Carolina at Greensboro Greensboro, NC 27402, U.S.A.

Fundamenta Mathematicae, Tome 212 (2011) no. 1, pp. 1-16.

Résumé

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

Détail

DOI : 10.4064/fm212-1-1

Keywords: main result states every fixed point continuous self map mathbb colorable result reformulated follows continuous map mathbb mathbb fixed point widetilde beta mathbb beta mathbb fixed point obtain generalization present examples