# FA19

Let $X\,$ and $Y\,$ be two normed spaces and $T\,$ be a linear mapping from $X\,$ to $Y\,$. Show that if $T\,$ is continuous, then the null space $N(T)\,$ is a closed subspace of $X\,$. Give an example showing that the closedness of $N(T)\,$ does not imply the continuity of $T\,$.