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Hi everyone: Suppose $E$ is a closed set with empty interior in $\mathbb{R}^{k}$, $k\geq2$. Can $\mathbb{R}^{k}\setminus E$ have infinitely many bounded components?

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Take $k=2$ and $E=\text{Grid}$, where $\text{Grid}:=\{(x,y) \mid x \text{ or }y \text{ is an integer}\}$.

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