## subspace existence which is NOT DENSE ? [closed]

please tell me whether converse of this is true or not ? "Let M be a subspace (may not be closed) of normed space X. show that M is not dense if there exist non zero functional from X* (the dual space of X) such that f(m)=0 , for all m belongs to M Required : if there exist non zero functional from X* (the dual space of X) such that f(m)=0 , for all m belongs to M then question arise whetherwe can conclude that M is not dense

-
Looks like homework. (Hint: Hahn-Banach) – Dick Palais Dec 20 2010 at 20:11
Let M be a subspace (may not be closed) of normed space X. show that M is not dense if{can we put here if and only if ???} there exist non zero functional from X* (the dual space of X) such that f(m)=0 , for all m belongs to M – sabyel Dec 20 2010 at 22:36
This is not a research-level question. Please see the FAQ. – Nate Eldredge Dec 20 2010 at 22:47