Let be a normed vector space and a closed subspace. Show that is also closed.

I was told to try using the Hahn-Banach theorem. So I know that there exists a function such that and . Where and

However, I don't see how to use this at all.

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- November 28th 2009, 03:40 PMputnam120Extending to closed space
Let be a normed vector space and a closed subspace. Show that is also closed.

I was told to try using the Hahn-Banach theorem. So I know that there exists a function such that and . Where and

However, I don't see how to use this at all. - November 29th 2009, 01:17 AMOpalg
- November 29th 2009, 04:10 PMputnam120
Thanks. In the time between our post I had figured out that I would have to show that a sequence of that form converged to a point in M. However, I was stuck at that part. (I was thinking about using the fact that the bounded linear functionals separate points somehow)