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Jordan curves and arcs and related material such as the Schoenflies theorem in dimension two.
4
votes
Accepted
A Jordan arc in the unit disk
It's certainly the case that $\mathbb{R}^2\setminus J$ is path connected.
So any two points in $D\setminus J$ are joined by a path in $\mathbb{R}^2$
missing $J$. If this path isn't in $D$ it hits the …