Is every finite dimensional subspace of a normed vector space closed? If yes, please prove it or else give a counter example.
2026-03-31 14:24:25.1774967065
closed subspace of normed vector space
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Finite dimensional normed spaces of the same dimension are isomorphic. A finite subspace of a normed vector space X is thus isomorphic to some $\ell_2^n$. As such, it is complete; thus closed.