Theorems · Theorem · functional analysis
ContinuousLinearMapWOT.toCLM_algebraMap
∀ {𝕜₁ : Type u_1} [inst : NormedField 𝕜₁] {E : Type u_3} [inst_1 : AddCommGroup E] [inst_2 : TopologicalSpace E]
[inst_3 : Module 𝕜₁ E] {S : Type u_5} [inst_4 : CommSemiring S] [inst_5 : Module S E] [inst_6 : SMulCommClass 𝕜₁ S E]
[inst_7 : SMul S 𝕜₁] [inst_8 : IsScalarTower S 𝕜₁ E] [inst_9 : ContinuousConstSMul S E]
[inst_10 : IsTopologicalAddGroup E] (c : S), ((algebraMap S (E →WOT[𝕜₁] E)) c).toCLM = (algebraMap S (E →L[𝕜₁] E)) c- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- ContinuousLinearMapstatement · cited by 5,352
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- IsTopologicalAddGroupstatement and proof · cited by 1,394
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