I want a correct reference to the next apparent reality:
An motion of a bunch $G$ on a compact metrizable house $Ok$ is topologically transitive (= the orbit of any nonempty open set is dense) if and provided that it the orbit $Gx$ of some level $xin Ok$ is dense in $Ok$.
For a cyclic group this characterization is proved right here. I hope that some textbook in topological dynamics ought to comprise such a fundamental reality. Please assist!
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