# Interpolating arc in path-connected set of ${\mathbb R}^n$

I know that in ${\mathbb R}^n$ (as in any Hausdorff space), a path-connected subset $A$ is automatically arc-connected also.

Is it also true that, given any finite subset $B$ of $A$, there is an arc passing through all the points of $B$?

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No, consider a cross in $\mathbb{R}^2$ as $A$ and the set of its four endpoints as $B$.