Minimal space with non-minimal square

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.

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