Minimal space with non-minimal square
Dynamical Systems
2020-05-27 v2
Abstract
We completely solve the problem whether the product of two compact metric spaces admitting minimal maps also admits a minimal map. Recently Boro\'nski, Clark and Oprocha gave a negative answer in the particular case when homeomorphisms rather than continuous maps are considered. In the present paper we show that there is a metric continuum admitting a minimal map, in fact a minimal homeomorphism, such that does not admit any minimal map.
Cite
@article{arxiv.1803.06323,
title = {Minimal space with non-minimal square},
author = {Ľubomír Snoha and Vladimír Špitalský},
journal= {arXiv preprint arXiv:1803.06323},
year = {2020}
}
Comments
This preprint has never been submitted to a journal. An improved version of it, with stronger results, is a part of the preprint Minimal direct products (arXiv:2005.06969 [math.DS])