Borel complexity up to the equivalence

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422270" target="_blank" >RIV/00216208:11320/20:10422270 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=WeiNLHP540" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=WeiNLHP540</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2019.107042" target="_blank" >10.1016/j.topol.2019.107042</a>

Result language
angličtina
Original language name
Borel complexity up to the equivalence
Original language description
We say that two classes of topological spaces are equivalent if each member of one class has a homeomorphic copy in the other class and vice versa. Usually when the Borel complexity of a class of metrizable compacta is considered, the class is realized as the subset of the hyperspace K([0, 1](omega)) containing all homeomorphic copies of members of the given class. We are rather interested in the lowest possible complexity among all equivalent realizations of the given class in the hyperspace. We recall that to every analytic subset of K([0,1](omega)) there exists an equivalent G(delta) subset. Then we show that up to the equivalence open subsets of the hyperspace K([0, 1](omega)) correspond to countably many classes of metrizable compacta. Finally we use the structure of open subsets up to equivalence to prove that to every F-sigma subset of K((0, 1](omega)) there exists an equivalent closed subset. (C) 2019 Elsevier B.V. All rights reserved.
Czech name
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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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