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I'm taking a new course on functional analysis and meet with the following problem.

If $X$ is a normed space (not necessarily complete), then prove that $X'$ is a Banach space.

Definition: When the induced metric space is complete,the normed space is called a Banach space. I don't have idea here,in particular I don't know what does $X'$ stands for? Regards!

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    It's the continuous dual.2012-04-14
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    To expand a bit on Alex's comment, $X'$ is the space of bounded linear maps $f: X \to \mathbb{C}$ with norm $\| f \| := \sup_{\| x \| \leq 1} |f(x)|$.2012-04-14

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