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arXiv · 1803.06323

Minimal space with non-minimal square

Ľubomír Snoha·Vladimír Špitalský
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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 $X$ admitting a minimal map, in fact a minimal homeomorphism, such that $X\times X$ does not admit any minimal map.

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Ľubomír Snoha, Vladimír Špitalský. 2018-03-16. Minimal space with non-minimal square. https://arxiv.org/abs/1803.06323

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