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I need your help with this problem that I founded it in a lecture notes. Then, the problem says:

Let $ X $ be a normed space. Show that if a sequence $ (x_n) _ {n \in \mathbb {N}} $ in $ X $ converges weakly to $ x $ then $ x\in Y $, where $ Y $ is the closure of the vector space generated by $\{x_n : n \in \mathbb{N} \} $.

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    what have you done?2012-08-28
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    For convex sets, the norm closure coincides with the weak closure.2012-08-28
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    @Holdsworth88 I should review all topics of my courses undergraduate for a exam that I have that pass, is the final, so I don't have much time, and I'm here, because with your help I could get it. For make this review quickly. Excuse me.2012-08-29

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