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Confusing notions of closed

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Poirot

Banned
Feb 15, 2012
250
I'm working in a normed space X. A subset E of X is closed if it's complement in X is open.
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?
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621