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Let (V, |· |v ) and (W, |· |w ) be normed vector spaces. Let T...

Let (V, |· |v ) and (W, |· |w ) be normed vector spaces. Let T : V → W be linear map. The kernel of T, denoted ker(T), is defined to be the set ker(T) = {v ∈ V : T(v) = 0}. Then ker(T) is a linear subspace of V .

Let W be a closed subspace of V with W not equal to V . Prove that W is nowhere dense in V .

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