Topological Vector Spaces/Direct sums

Exercises

 * 1) Let $$E$$ be a TVS. Prove that all finite-dimensional subspaces of $$E$$ have a topological complement if and only if for every $$x \notin \overline{\{0\}}$$, there exists $$x' \in E'$$ so that $$x'(x) \neq 0$$.