Originally Posted by

**math8** Thanks, this makes a lot of sense.

But how do I show that |f|< or equal to 1/d where d= distance(z,F)

I know it involves some corollary to the Hahn-Banach theorem:

" If Y is a linear subspace of the normed space X, x is in X and d=dist(x,Y)>0, then there exists x* in X* such that x*(x)=1 and |x*|=1/d and x*|Y=0 (x* restricted to Y is 0)".

I think maybe the reason we want this to be true is that in that case, f would be bounded hence continuous, thus f is in the dual S*.

But how does this help?