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 Boro\'nski, Clark and Oprocha gave a negative answer in the particular case when homeomorphisms rather than continuous maps are considered. In the present...
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| creator | Snoha, Ľubomír Špitalský, Vladimír |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1803.06323 |
| format | Article |
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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
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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
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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.</abstract><doi>10.48550/arxiv.1803.06323</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Dynamical Systems |
| title | Minimal space with non-minimal square |
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