Let $A$ and $B$ be two unital Banach algebras and $T\colon A\to B$ an homomorphism of Banach algebras. Let denote the set of Fredholm perturbation elements in $A$, i.e.
$\operatorname{Ft}:=\{r\in A:T(a+r)\mbox{ is invertible in }B \mbox{ iff }T(a) \mbox{ is invertible in }B\}$.
I NEED a clear answer for this questions :
Why $\operatorname{Ft}$ is closed?
Please help me.