Pointwise-bounded family of bounded operators on Banach space is uniformly-bounded in operator-norm. Baire-category argument. Foundational of three classical theorems (with open-mapping + closed-graph).
Pointwise-bounded family of bounded operators on Banach space is uniformly-bounded in operator-norm. Baire-category argument. Foundational of three classical theorems (with open-mapping + closed-graph).