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.
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)