Minimal space with non-minimal square

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 w...

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Veröffentlicht in:arXiv.org 2020-05
Hauptverfasser: Snoha, Ľubomír, Špitalský, Vladimír
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description 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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