Fixed-point free maps of Euclidean spaces

2010/11/23 by R. Z. Bouziakova, Bouziakova, R. Z., Alex Chigogidze +2
Mathematics · #54H25 #58C30 #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Mathematics and Applications #math.GN #msc:54H25 #msc:58C30

paper · pdf · doi:10.48550/arxiv.1011.4990

arxiv created 2010/11/23 · openalex publication_date 2010/11/23 · arxiv updated 2010/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our main result states that every fixed-point free continuous self-map of \mathbb Rⁿ is colorable. This result can be re-formulated as follows: A continuous map f: \mathbb Rⁿ→ \mathbb Rⁿ is fixed-point free iff \widetilde f: β\mathbb Rⁿ→ β\mathbb Rⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples.

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