Theorems · Theorem · functional analysis
SpectrumRestricts.continuous_starAlgHom
∀ {R : Type u_1} {S : Type u_2} {A : Type u_3} [inst : Semifield R] [inst_1 : StarRing R] [inst_2 : MetricSpace R]
[inst_3 : IsTopologicalSemiring R] [inst_4 : ContinuousStar R] [inst_5 : Semifield S] [inst_6 : StarRing S]
[inst_7 : MetricSpace S] [inst_8 : IsTopologicalSemiring S] [inst_9 : ContinuousStar S] [inst_10 : Ring A]
[inst_11 : StarRing A] [inst_12 : Algebra S A] [inst_13 : Algebra R S] [inst_14 : Algebra R A]
[inst_15 : IsScalarTower R S A] [inst_16 : StarModule R S] [inst_17 : ContinuousSMul R S]
[inst_18 : TopologicalSpace A] {a : A} {φ : C(↑(spectrum S a), S) →⋆ₐ[S] A},
Continuous ⇑φ → ∀ {f : C(S, R)} (h : SpectrumRestricts a ⇑f), Continuous ⇑(SpectrumRestricts.starAlgHom φ h)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Set.Elemstatement and proof · cited by 7,166
- IsScalarTowerstatement and proof · cited by 3,896
- Continuousstatement and proof · cited by 2,592
- ContinuousMapstatement and proof · cited by 2,491
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
- ContinuousSMulstatement and proof · cited by 1,016
Cited by2
Results whose statement or proof uses this declaration.
- SpectrumRestricts.cfcHom_eq_restrictproof · cited by 5
- SpectrumRestricts.cfcproof · cited by 2