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The convex hull of a set $X$ of points in a Euclidean space is the smallest convex set that contains $X$.

21 votes

Convex Hull of Path Connected sets

This is true in $\mathbb R^2$ but not in higher dimensions. For example, consider a path in $\mathbb R^3$ that lies in the half-space $z\ge 0$ and touches the $xy$-plane at three non-collinear points. …
Sergei Ivanov's user avatar