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2020 Sectional category and the fixed point property
Cesar A. Ipanaque Zapata, Jesús González
Topol. Methods Nonlinear Anal. 56(2): 559-578 (2020). DOI: 10.12775/TMNA.2020.033

Abstract

For a Hausdorff space $X$, we exhibit an unexpected connection between the sectional number of the Fadell-Neuwirth fibration $\pi_{2,1}^X\colon F(X,2)\to X$, and the fixed point property (FPP) for self-maps on $X$. Explicitly, we demonstrate that a space $X$ has the FPP if and only if 2 is the minimal cardinality of open covers $\{U_i\}$ of $X$ such that each $U_i$ admits a continuous local section for $\pi_{2,1}^X$. This characterization connects a standard problem in fixed point theory to current research trends in topological robotics.

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Cesar A. Ipanaque Zapata. Jesús González. "Sectional category and the fixed point property." Topol. Methods Nonlinear Anal. 56 (2) 559 - 578, 2020. https://doi.org/10.12775/TMNA.2020.033

Information

Published: 2020
First available in Project Euclid: 5 December 2020

Digital Object Identifier: 10.12775/TMNA.2020.033

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.56 • No. 2 • 2020
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