Solution
= Solution
If $\|Tx\|\ge\delta\|x\|$ and $\|S-T\|<\delta$, then
$\|Sx\|\ge(\delta-\|S-T\|)\|x\|$. Thus bounded-below maps form an <open set>.
= Solution
If $\|Tx\|\ge\delta\|x\|$ and $\|S-T\|<\delta$, then
$\|Sx\|\ge(\delta-\|S-T\|)\|x\|$. Thus bounded-below maps form an <open set>.