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Dec 12, 2020 at 0:49 vote accept M. Rahmat
Dec 11, 2020 at 18:00 comment added M. Rahmat The complement of $F$ must be connected. Is this the case here?
Dec 11, 2020 at 7:28 comment added Nate Eldredge Or in $n=2$, an almost-complete arc of a circle, together with some ray heading to infinity to make it unbounded.
Dec 11, 2020 at 7:11 answer added Anthony Quas timeline score: 3
Dec 11, 2020 at 7:05 comment added Anthony Quas How about $n=3$, $F$ consists of the $x$-axis from $-\infty$ to $-2$ followed by a 0.1-dense continuous curve on the sphere of radius 2 about the origin followed by a line from 2 to $\infty$; and $\delta=1$. There is a component of $A$ inside the sphere (close to the unit sphere) and there is a component outside the sphere.
Dec 11, 2020 at 6:50 history asked M. Rahmat CC BY-SA 4.0