Fixed-point free maps of Euclidean spaces
Fundamenta Mathematicae, Tome 212 (2011) no. 1, pp. 1-16
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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
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
Affiliations des auteurs :
R. Z. Buzyakova 1 ; A. Chigogidze 1
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author = {R. Z. Buzyakova and A. Chigogidze},
title = {Fixed-point free maps of {Euclidean} spaces},
journal = {Fundamenta Mathematicae},
pages = {1--16},
publisher = {mathdoc},
volume = {212},
number = {1},
year = {2011},
doi = {10.4064/fm212-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm212-1-1/}
}
R. Z. Buzyakova; A. Chigogidze. Fixed-point free maps of Euclidean spaces. Fundamenta Mathematicae, Tome 212 (2011) no. 1, pp. 1-16. doi: 10.4064/fm212-1-1
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