topological stable rank one and AF-algebra construction on Cantor set

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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