Minimality for actions of abelian semigroups on compact spaces with a free interval

Mat\'u\v{s} Dirb\'ak; Peter Mali\v{c}k\'y; Roman Hric; Vladim\'ir \v{S}pitalsk\'y; \v{L}ubom\'ir Snoha

arxiv: 1703.10445 · v2 · pith:PTUUIMJSnew · submitted 2017-03-30 · 🧮 math.DS

Minimality for actions of abelian semigroups on compact spaces with a free interval

Mat\'u\v{s} Dirb\'ak , Roman Hric , Peter Mali\v{c}k\'y , \v{L}ubom\'ir Snoha , Vladim\'ir \v{S}pitalsk\'y This is my paper

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keywords abelianactionsfreeintervalsemigroupscompactminimalminimality

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We study minimality for continuous actions of abelian semigroups on compact Hausdorff spaces with a free interval. First, we give a necessary and sufficient condition for such a space to admit a minimal action of a given abelian semigroup. Further, for actions of abelian semigroups we provide a trichotomy for the topological structure of minimal sets intersecting a free interval.

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Minimality for actions of abelian semigroups on compact spaces with a free interval

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