A Sternbach-type fixed point problem for maps induced on hyperspaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F20%3AA2101O4M" target="_blank" >RIV/61988987:17610/20:A2101O4M - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0166864120302479" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0166864120302479</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2020.107304" target="_blank" >10.1016/j.topol.2020.107304</a>

Result language
angličtina
Original language name
A Sternbach-type fixed point problem for maps induced on hyperspaces
Original language description
We show that for any map f on an arc-like continuum X, the induced map on the hyperspace of subcontinua fixes a point in any -invariant subcontinuum of . This extends a result of Robatian, who proved it for the arc. However, as we show, the result does not extend to tree-like continua. We conclude with a list of related problems. Our proof builds on Hamilton's proof of the fixed point property of arc-like continua.
Czech name
—
Czech description
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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

Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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