Does closed imply bounded?

The set $\{\,(x,y)\in\mathbb R^2\mid xy=1\,\}$ is closed but not bounded.

Even simpler, $\mathbb R^n$ itself is closed (but not bounded).


$\mathbb{R}^m$ itself is a closed set. is it bounded?

But in case of Compact sets, they are closed as well as bounded in $\mathbb{R}^n$.

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General Topology

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