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  "body": "\n## Summary\n\nA minimal set of a continuous map is a nonempty closed [[invariant set|WWZTW11664]] that contains no smaller nonempty closed invariant set.\nEquivalently, the forward orbit of each of its points is dense in it.\nMinimal sets are the smallest building blocks of [[topological dynamics|5X6E97EMFR]].\nOn a nonempty compact space every continuous map has at least one minimal set, by Zorn's lemma.\n\n## Explanations\n\n### L1 human\n\nA minimal set is a piece of the space that the motion cannot split further.\nStart anywhere in it, and the orbit comes as close as you like to every point of it.\nA periodic orbit is a minimal set: it is finite, closed and invariant, and any invariant subset contains a whole orbit.\nFor an irrational rotation of the circle, the whole circle is a minimal set, because every orbit is dense.\n",
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