The complexity of homeomorphism relations on some classes of compacta with bounded topological dimension

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475476" target="_blank" >RIV/00216208:11320/23:10475476 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=e1-6DJbItm" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=e1-6DJbItm</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4064/fm164-8-2023" target="_blank" >10.4064/fm164-8-2023</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The complexity of homeomorphism relations on some classes of compacta with bounded topological dimension

Popis výsledku v původním jazyce

We are dealing with the complexity of the homeomorphism relation onsome classes of metrizable compacta from the viewpoint of invariant descriptive set theory.We prove that the homeomorphism relation for absolute retracts in the plane is Borelbireducible with the isomorphism relation for countable graphs. In order to stress thesharpness of this result, we prove that neither the homeomorphism relation for locallyconnected continua in the plane nor the homeomorphism relation for absolute retracts in R3is Borel reducible to the isomorphism relation for countable graphs.We also improve recentresults of Chang and Gao by constructing a Borel reduction from both the homeomorphismrelation for compact subsets of Rn and the ambient homeomorphism relation for compactsubsets of [0, 1]n to the homeomorphism relation for n-dimensional continua in [0, 1]n+1.

Název v anglickém jazyce

The complexity of homeomorphism relations on some classes of compacta with bounded topological dimension

Popis výsledku anglicky

We are dealing with the complexity of the homeomorphism relation onsome classes of metrizable compacta from the viewpoint of invariant descriptive set theory.We prove that the homeomorphism relation for absolute retracts in the plane is Borelbireducible with the isomorphism relation for countable graphs. In order to stress thesharpness of this result, we prove that neither the homeomorphism relation for locallyconnected continua in the plane nor the homeomorphism relation for absolute retracts in R3is Borel reducible to the isomorphism relation for countable graphs.We also improve recentresults of Chang and Gao by constructing a Borel reduction from both the homeomorphismrelation for compact subsets of Rn and the ambient homeomorphism relation for compactsubsets of [0, 1]n to the homeomorphism relation for n-dimensional continua in [0, 1]n+1.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fundamenta Mathematicae

ISSN

0016-2736

e-ISSN

1730-6329

Svazek periodika

263

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

22

Strana od-do

1-22

Kód UT WoS článku

001080446500001

EID výsledku v databázi Scopus

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