Theorems · Theorem · functional analysis
WeakDual.CharacterSpace.compContinuousMap_id
∀ (A : Type u_1) {𝕜 : Type u_4} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[inst_3 : CompleteSpace A] [inst_4 : StarRing A],
WeakDual.CharacterSpace.compContinuousMap (StarAlgHom.id 𝕜 A) = ContinuousMap.id ↑(WeakDual.characterSpace 𝕜 A)WeakDual.CharacterSpace.compContinuousMap sends the identity to the identity.
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- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.Elemstatement and proof · cited by 7,166
- CompleteSpacestatement and proof · cited by 2,532
- ContinuousMapstatement · cited by 2,491
- StarRingstatement and proof · cited by 1,686
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- WeakDualstatement · cited by 103
- ContinuousMap.extproof · cited by 92
- ContinuousMap.idstatement · cited by 73
- WeakDual.characterSpacestatement and proof · cited by 39
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