A compact minimal space Y such that its square Y xY is not minimal

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F18%3AA1901JNM" target="_blank" >RIV/61988987:17610/18:A1901JNM - isvavai.cz</a>

Výsledek na webu

<a href="https://arxiv.org/abs/1612.09179" target="_blank" >https://arxiv.org/abs/1612.09179</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aim.2018.07.011" target="_blank" >10.1016/j.aim.2018.07.011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A compact minimal space Y such that its square Y xY is not minimal

Popis výsledku v původním jazyce

The following well known open problem is answered in the negative: Given two compact spaces X and Y that admit minimal homeomorphisms, must the Cartesian product X x Y admit a minimal homeomorphism as well? Moreover, it is shown that such spaces can be realized as minimal sets of torus homeomorphisms homotopic to the identity. A key element of our construction is an inverse limit approach inspired by combination of a technique of Aarts & Oversteegen and the construction of Slovak spaces by Downarowicz & Snoha & Tywoniuk. This approach allows us also to prove the following result. Let g: M x R -> M be a continuous, aperiodic minimal flow on the compact, finite-dimensional metric space M. Then there is a generic choice of parameters c is an element of R, such that the homeomorphism h(x) = g(x, c) admits a noninvertible minimal map f : M -> M as an almost 1-1 extension.

Název v anglickém jazyce

A compact minimal space Y such that its square Y xY is not minimal

Popis výsledku anglicky

The following well known open problem is answered in the negative: Given two compact spaces X and Y that admit minimal homeomorphisms, must the Cartesian product X x Y admit a minimal homeomorphism as well? Moreover, it is shown that such spaces can be realized as minimal sets of torus homeomorphisms homotopic to the identity. A key element of our construction is an inverse limit approach inspired by combination of a technique of Aarts & Oversteegen and the construction of Slovak spaces by Downarowicz & Snoha & Tywoniuk. This approach allows us also to prove the following result. Let g: M x R -> M be a continuous, aperiodic minimal flow on the compact, finite-dimensional metric space M. Then there is a generic choice of parameters c is an element of R, such that the homeomorphism h(x) = g(x, c) admits a noninvertible minimal map f : M -> M as an almost 1-1 extension.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

ADV MATH

ISSN

0001-8708

e-ISSN

—

Svazek periodika

335

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

261-275

Kód UT WoS článku

000442061400010

EID výsledku v databázi Scopus

2-s2.0-85049802014