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Started topologically cyclic group, as needed at global family.
(never mind)
Does a topological cyclic group retain the meaning of a cyclic group as having only one-generator?
Or can we have, for example, a free group on 2-generators that is “topologically cyclic” if we can map it to a circle?
The one generator subgroup must be dense. Think of an irrational in under addition.
Or even any torus: if you pick a point in whose coordinates are sufficiently linearly independent, then the closure of the orbit under the -action will be dense in the torus.
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