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I quote an unsolved question posted in MHF (November 19th, 2012) by user

**machi**.I have a problem to proof this theorem, Anyone can help for detail.

"A subspace Y of Banach space X is complete if and only if Y is closed in X"

I have an idea to prove this theorem, but I am not sure about this and I can't wrote it for detail.

Please correct my answer,

from left to right "let [tex]X [/tex]is Banach space, [tex]Y\subset X[/tex]. so, [tex]Y[/tex] is Banach space. consider of Banach space definition, every Cauchy sequence of [tex]Y[/tex] is converge to [tex]x\in X[/tex] then [tex]Y[/tex] is closed on [tex]X[/tex]".

right to left "I am still totally confuse..."

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