dc.contributor.author | Boroński, JP | en_US |
dc.contributor.author | Clark, A | en_US |
dc.contributor.author | Oprocha, P | en_US |
dc.date.accessioned | 2019-06-27T08:18:21Z | |
dc.date.available | 2018-07-03 | en_US |
dc.date.issued | 2018-09-07 | en_US |
dc.identifier.issn | 1090-2082 | en_US |
dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/58237 | |
dc.description.abstract | © 2018 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×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 ϕ:M×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∈R, such that the homeomorphism h(x)=ϕ(x,c) admits a noninvertible minimal map f:M→M as an almost 1-1 extension. | en_US |
dc.format.extent | 261 - 275 | en_US |
dc.publisher | Elsevier | en_US |
dc.relation.ispartof | Advances in Mathematics | en_US |
dc.rights | https://doi.org/10.1016/j.aim.2018.07.011 | |
dc.title | A compact minimal space Y such that its square Y × Y is not minimal | en_US |
dc.type | Article | |
dc.rights.holder | © 2018 Elsevier Inc. | |
dc.identifier.doi | 10.1016/j.aim.2018.07.011 | en_US |
pubs.notes | Not known | en_US |
pubs.publication-status | Published | en_US |
pubs.volume | 335 | en_US |
dcterms.dateAccepted | 2018-07-03 | en_US |
rioxxterms.funder | Default funder | en_US |
rioxxterms.identifier.project | Default project | en_US |