# gn.common topology – Connecting a compact subset by a unostentatious round Answer

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gn.common topology – Connecting a compact subset by a unostentatious round

Let $$Okay$$ breathe a compact subset of $$mathbb R^n$$ (say for those who love $$n=2$$, which is probably sufficiently consultant).

Q: Does there live a closed unostentatious round $$u:mathbb S^1tomathbb R^n$$ such that $$Kcup u(mathbb S^1 )$$ is related?

The clique $$Okay$$ could have uncountably many related elements, and $$u$$ has to proper all of them. Yet this doesn’t appear a sober obstruction. For occasion, the cartesian sq. of the Cantor clique can breathe related by some unostentatious self-similar round (essentially of innumerable size; in reality I cerebrate of dimension a minimum of $$4/3$$), e.g. simply connecting suitably the 4 important sq. clusters between them by segments, after which iterating.

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