Borel complexity up to the equivalence

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Borel complexity up to the equivalence

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Borel complexity up to the equivalence

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Topology and its Applications

ISSN

0166-8641

e-ISSN

—

Svazek periodika

270

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

13

Strana od-do

107042

Kód UT WoS článku

000514019400017

EID výsledku v databázi Scopus

2-s2.0-85076909884