V is a vector space over the field F. W is a proper subspace of V. Does there exist a subspace U such that V is the direct sum of U and W. I have been able to prove that such a subspace exists in the finite dimensional case. Can I get a hint on how to proceed in the non-finite dimensional case?
2026-03-26 17:35:11.1774546511
Existence of subspace
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Proceed as in the finite dimensional case: extend a basis of $W$ to a basis of $V$.