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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - 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

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Name of the periodical

Fundamenta Mathematicae

ISSN

0016-2736

e-ISSN

1730-6329

Volume of the periodical

263

Issue of the periodical within the volume

1

Country of publishing house

PL - POLAND

Number of pages

22

Pages from-to

1-22

UT code for WoS article

001080446500001

EID of the result in the Scopus database

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