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A note on fixed points of abelian actions in dimension one


Author: J. P. Boroński
Journal: Proc. Amer. Math. Soc. 147 (2019), 1653-1655
MSC (2010): Primary 37B05, 37B45
DOI: https://doi.org/10.1090/proc/14365
Published electronically: December 12, 2018
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Abstract: The result of Boyce and Huneke gives rise to a 1-dimensional continuum, which is the intersection of a descending family of disks that admits two commuting homeomorphisms without a common fixed point.


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Additional Information

J. P. Boroński
Affiliation: National Supercomputing Centre IT4Innovations, Division of the University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava, Czech Republic – and – Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
Email: jan.boronski@osu.cz

DOI: https://doi.org/10.1090/proc/14365
Keywords: Commuting homeomorphisms, fixed point
Received by editor(s): March 25, 2018
Received by editor(s) in revised form: August 15, 2018
Published electronically: December 12, 2018
Additional Notes: The author was supported by University of Ostrava grant lRP201824 “Complex topological structures” and the NPU II project LQ1602 IT4Innovations excellence in science.
Communicated by: Nimish Shah
Article copyright: © Copyright 2018 American Mathematical Society