Theorems · Theorem · functional analysis

IsBoundedBilinearMap.continuous

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : Semiring 𝕜] [inst_1 : SeminormedAddCommGroup E]
  [inst_2 : Module 𝕜 E] [inst_3 : SeminormedAddCommGroup F] [inst_4 : Module 𝕜 F] [inst_5 : SeminormedAddCommGroup G]
  [inst_6 : Module 𝕜 G] {f : E × F → G}, IsBoundedBilinearMap 𝕜 f → Continuous f

Useful to use together with Continuous.comp₂.

Defined in

Mathlib.Analysis.Normed.Operator.BoundedLinearMaps

Cited by

11 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSeminormedAddCommGroupModuleSeminormedAddCommGroupModuleSeminormedAddCommGroupModule