Theorem: Let $T:X\rightarrow Y$ be linear operator. Show that if $T$ is continous on X, then it is bounded.
The attempt:
if $T$ is continous on X, it is contionous at origin. Then, $\forall x\in X $ we have $\lVert T(x)\rVert<\epsilon $ where $\lVert x\rVert <\delta$,
we must show that there is a $C>0$ such that for $\forall x\in X $, $ \lVert A (x)\rVert <C \lVert x\rVert $. How?
