Could someone give me a hand on this problem? I want to show that the set in complete in

I tried to show that any convergent sequence in must have its limit in which means is closed in a complete space, but I failed to do this.

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- Dec 10th 2011, 09:54 PMjackieComplete subset
Could someone give me a hand on this problem? I want to show that the set in complete in

I tried to show that any convergent sequence in must have its limit in which means is closed in a complete space, but I failed to do this. - Dec 10th 2011, 10:20 PMFernandoRevillaRe: Complete subset
- Dec 11th 2011, 06:26 PMjackieRe: Complete subset
- Dec 11th 2011, 09:58 PMDrexel28Re: Complete subset
Presumably is . Note then that since is itself, you have that a given subspace is complete if and only if it's closed. But, evidently is closed since the mapping is a continuous (linear functional) map , and is the preimage of the closed set under this map.

- Dec 11th 2011, 11:08 PMFernandoRevillaRe: Complete subset