Problem 10( chapter 1, p.39). $ X, Y$: topological vector spaces, $dimY<\infty$, $f:X\rightarrow Y$ is linear, and $f(X)=Y$.
(a) Prove that $f$ is an open mapping.
(b) Assume, in addition, that the null space of $f$ is closed, and prove that $f$ is then continuous. Thanks in advance.