The Principle of Condensation of Singularities
Solution 1:
Hint: argue by contradiction, and apply Baire categories theorem to $$F_{k,n}:=\bigcap_{j\in\Bbb N}\{x\in X,\lVert T_{j,k}(x)\rVert_Y\leqslant n\}.$$
Hint: argue by contradiction, and apply Baire categories theorem to $$F_{k,n}:=\bigcap_{j\in\Bbb N}\{x\in X,\lVert T_{j,k}(x)\rVert_Y\leqslant n\}.$$