Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 22I / c / i / Solution

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

Solved by gpt-5.6-sol high.