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I've also read that in an inner product space, a set E is closed if all convergent sequences in E converge to something in E.

My question is, for a normed space X, are these 2 definitions equivalent?

- Thread starter Poirot
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I've also read that in an inner product space, a set E is closed if all convergent sequences in E converge to something in E.

My question is, for a normed space X, are these 2 definitions equivalent?

- Feb 5, 2012

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Hi Poirot,

I've also read that in an inner product space, a set E is closed if all convergent sequences in E converge to something in E.

My question is, for a normed space X, are these 2 definitions equivalent?

Yes they are. Refer Lemma 2.2.3 on the following link.

http://www.google.ca/url?sa=t&rct=j...DgUUKXmasG-n7lCX-1BYqDw&bvm=bv.53537100,d.dmg