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Let $E$ be a normed space and $F$ be a subspace of $E$. Show that $F$ is dense in $E$ if and only if all the linear and continuous functional on $E$ satisfying $f\vert _F=0 $ are identically zero ($f = 0$).

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    i think it related to Hahn - Banach extension on $ l_p $ to $ c_0$ because $ l_p$ is dense in $ c_0$, so all extensions are unique and itself.2012-12-18

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