Always exist a curve in compact and convex subset of $\mathbb{R}^3$?
2026-04-02 22:57:21.1775170641
Jordan curves in compact subset in $\mathbb R^3$
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If the set contains three non-collinear points, then it contains a triangle, and the answer is clearly yes.
If the set does not contain three non-collinear points then it is a closed segment or a point. If you are looking for closed simple curves, then in this case the answer is no.