# How to extend $f\in M^*$ to $\overline{M}$? [closed]

Let $X$ be a locally convex space, let $M$ be a linear subspace of $X$, and let $f\in M^*$.

If $M$ is closed, then $M=\overline{M}$. And we don't have to extend $f$. So how to extend $f$ to $\overline{M}$ if $M$ is not closed?

• In fact, you can use the analytic form of the Hahn-Banach theorem to obtain an extension $F \colon X \rightarrow \mathbb{K}$ of $f \colon M \rightarrow \mathbb{K}$ on all of $X$. – p4sch Sep 4 '18 at 20:37