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

作者：Boronski J P; Clark Alex; Oprocha P^*

来源：Advances in Mathematics, 2018, 335: 261-275.

DOI：10.1016/j.aim.2018.07.011

• Minimal maps

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 phi: 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) = phi(x, c) admits a noninvertible minimal map f : M -> M as an almost 1-1 extension.

• 出版日期2018-9-7