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If $S\subseteq\mathbb{R}^n$ and $\vec{a}\in S$ such that $B_r(\vec{a})\in S$ for some $r>0$, then $\vec{a}$ is an interior point of $S$.
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If $S\subseteq\mathbb{R}^n$ and $\vec{a}\in S$ such that $B_r(\vec{a})\in S$ for some $r>0$, then $\vec{a}$ is an interior point of $S$.
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