Hey guys,

Let A be a linear operator from a vector space X into a vector space Y, and define also \mathcal{B}(X,Y) as the vector space of all bounded linear operators. Now, a set of notes claims the following

"If X and Y are normed spaces, and A \in \mathcal{B}(X,Y), then Ker (A) is closed; this is not necessarily true for Ran (A)."

Why is this the case?

Thanks a lot in advance,