Minimal space with non-minimal square

Abstract

We completely solve the problem whether the product of two compact metric spaces admitting minimal maps also admits a minimal map. Recently Boroński, 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 $X$ admitting a minimal map, in fact a minimal homeomorphism, such that $X\times X$ does not admit any minimal map.

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])