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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