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Theorems · Theorem · functional analysis

UniformSpace.Completion.continuous_inner

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E],
  Continuous (Function.uncurry (inner 𝕜))
Defined in
Mathlib.Analysis.InnerProductSpace.Completion
Cited by
1 results in Mathlib
Foundations
Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLikeSeminormedAddCommGroupInnerProductSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

UniformSpace.Completion.Continuous.inner · cited by 0Continuous.innerDFunLike.coe · cited by 62936DFunLike.coeInnerProductSpace · cited by 3523InnerProductSpaceAddMonoidHom · cited by 3230AddMonoidHomRCLike · cited by 2829RCLikeSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupContinuous · cited by 2592ContinuousInner.inner · cited by 1089Inner.innerUniformSpace.Completion · cited by 192UniformSpace.CompletionAddMonoidHom.ext · cited by 149AddMonoidHom.extLinearMap.toAddMonoidHom · cited by 101LinearMap.toAddMonoidHominner_zero_left · cited by 59inner_zero_leftIsDenseInducing.extend · cited by 29IsDenseInducing.extendinner_add_left · cited by 28inner_add_leftinnerₛₗ · cited by 28innerₛₗcontinuous_inner · cited by 15continuous_innerCompletion.continuous_innerCITED BYCITES

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.