On the number of orbits of the homeomorphism group of solenoidal spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F15%3AA150197J" target="_blank" >RIV/61988987:17610/15:A150197J - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On the number of orbits of the homeomorphism group of solenoidal spaces

Popis výsledku v původním jazyce

A continuum X is called solenoidal if it is circle-like and nonplanar. X is 1/n-homogeneous if the action of its homeomorphism group on X has exactly n orbits; i.e. there are exactly n types of points in X. Recently Jim'enez-Her'andez, Minc and Pellicer-Covarrubias [Topology and its Applications, 160 (2013) 930--936] constructed a family of 1/n-homogeneous solenoidal continua, for every n>2. Modifying the spaces obtained by them, as well as an earlier construction of the author for n=2, for every n>2we construct two different uncountable families of arcless 1/n-homogeneous solenoidal continua. We also show that there is an uncountable family of countably nonhomogeneous solenoidal continua. With respect to the degree of homogeneity, in the realm of solenoidal continua containing pseudoarcs, our examples complete the gap between homogeneous solenoids of pseudoarcs and uncountably nonhomogeneous pseudosolenoids. A number of questions related to the study is raised.

Název v anglickém jazyce

On the number of orbits of the homeomorphism group of solenoidal spaces

Popis výsledku anglicky

A continuum X is called solenoidal if it is circle-like and nonplanar. X is 1/n-homogeneous if the action of its homeomorphism group on X has exactly n orbits; i.e. there are exactly n types of points in X. Recently Jim'enez-Her'andez, Minc and Pellicer-Covarrubias [Topology and its Applications, 160 (2013) 930--936] constructed a family of 1/n-homogeneous solenoidal continua, for every n>2. Modifying the spaces obtained by them, as well as an earlier construction of the author for n=2, for every n>2we construct two different uncountable families of arcless 1/n-homogeneous solenoidal continua. We also show that there is an uncountable family of countably nonhomogeneous solenoidal continua. With respect to the degree of homogeneity, in the realm of solenoidal continua containing pseudoarcs, our examples complete the gap between homogeneous solenoids of pseudoarcs and uncountably nonhomogeneous pseudosolenoids. A number of questions related to the study is raised.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

TOPOL APPL

ISSN

0166-8641

e-ISSN

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Svazek periodika

182

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

98-106

Kód UT WoS článku

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EID výsledku v databázi Scopus

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