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# $\mathbb{R}^{n}$ is not a countable union of proper vector subspaces

$\mathbb{R}^{n}$ is not a countable union of proper vector subspaces.

Proof

We know that every finite dimensional proper subspace of a normed space is nowhere dense. Besides, $\mathbb{R}^{n}$ is a Banach space, so the results follows directly.

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## Mathematics Subject Classification

54E52*no label found*

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