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9. Suppose (a) X and Y are topological vector spaces (b) Λ : X-, Y is linear, (c) N is a closed subspace of X, (d) π: X → X/N is the quotient map, and (e) Ax 0 for every x E N Prove that there is a unique f:X/N→Y which satisfies A f.π, that is, Ax-:f.(n(x)) for all x E X. Prove that this fis linear and that Λ is continuous if and only if fis continuous. Also, Л is open if and only if/is open

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