Fixed-point free maps of Euclidean spaces

Volume 212 / 2011

R. Z. Buzyakova, A. Chigogidze 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

Authors

  • R. Z. BuzyakovaDepartment of Mathematics and Statistics
    The University of North Carolina at Greensboro
    Greensboro, NC 27402, U.S.A.
    e-mail
  • A. ChigogidzeDepartment of Mathematics and Statistics
    The University of North Carolina at Greensboro
    Greensboro, NC 27402, U.S.A.
    e-mail

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