Theorems · Theorem · functional analysis
cfcHomSuperset_continuous
∀ {R : Type u_1} {A : Type u_2} {p : A → Prop} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : MetricSpace R]
[inst_3 : IsTopologicalSemiring R] [inst_4 : ContinuousStar R] [inst_5 : Ring A] [inst_6 : StarRing A]
[inst_7 : TopologicalSpace A] [inst_8 : Algebra R A] [instCFC : ContinuousFunctionalCalculus R A p] {a : A} (ha : p a)
{s : Set R} (hs : spectrum R a ⊆ s), Continuous ⇑(cfcHomSuperset ha hs)- Cited by
- 0 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- Set.Elemstatement · cited by 7,166
- Continuousstatement · cited by 2,592
- ContinuousMapstatement · cited by 2,491
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
- ContinuousStarstatement and proof · cited by 543
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.