A compact minimal space Y such that its square Y xY is not minimal
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
A compact minimal space Y such that its square Y xY is not minimal
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ADV MATH
ISSN
0001-8708
e-ISSN
—
Volume of the periodical
335
Issue of the periodical within the volume
9
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
261-275
UT code for WoS article
000442061400010
EID of the result in the Scopus database
2-s2.0-85049802014