Let $A$ be a closed set in $\mathbb{R}^n$ such that $0\notin A$. Can we deduce that the set $B=\{\frac{x}{\|x\|}:\, x\in A\}$ is also closed? Thank you in advance.
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Let $A$ be a closed set in $\mathbb{R}^n$ such that $0\notin A$. Can we deduce that the set $B=\{\frac{x}{\|x\|}:\, x\in A\}$ is also closed? Thank you in advance.