Every continuous action of a compact group on a uniquely arcwise connected continuum has a fixed point
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10390806" target="_blank" >RIV/00216208:11320/18:10390806 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11784-018-0552-3" target="_blank" >https://doi.org/10.1007/s11784-018-0552-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11784-018-0552-3" target="_blank" >10.1007/s11784-018-0552-3</a>
Alternative languages
Result language
angličtina
Original language name
Every continuous action of a compact group on a uniquely arcwise connected continuum has a fixed point
Original language description
We are dealing with the question whether every group or semigroup action (with some additional property) on a continuum (with some additional property) has a fixed point. One of such results was given in 2009 by Shi and Sun. They proved that every nilpotent group action on a uniquely arcwise connected continuum has a fixed point. We are seeking for this type of results with, e.g., commutative, compact, or torsion groups and semigroups acting on dendrites, dendroids, -dendroids and uniquely arcwise connected continua. We prove that every continuous action of a compact or torsion group on a uniquely arcwise connected continuum has a fixed point. We also prove that every continuous action of a compact and commutative semigroup on a uniquely arcwise connected continuum or on a tree-like continuum has a fixed point.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ17-04197Y" target="_blank" >GJ17-04197Y: Dynamical systems and Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Fixed Point Theory and Applications
ISSN
1661-7738
e-ISSN
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Volume of the periodical
20
Issue of the periodical within the volume
2
Country of publishing house
CH - SWITZERLAND
Number of pages
9
Pages from-to
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UT code for WoS article
000434684300020
EID of the result in the Scopus database
2-s2.0-85045530466