Let $E$, $F$ be normed vector spaces and $M$ a subspace of $E$.
I'm trying to find an example of a function $f:M\to F$ such that $f$ is linear and continuous but that you can't extend it to $\tilde{f}: E\to F$ linear and continuous.
I already know that you can extend every linear function into another linear function but I can't find and example where the continuity fails.