Theorems · Theorem · functional analysis
cfc_apply_zero
∀ {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 : TopologicalSpace A] [inst_6 : Ring A]
[inst_7 : StarRing A] [inst_8 : Algebra R A] [instCFC : ContinuousFunctionalCalculus R A p] {f : R → R},
cfc f 0 = (algebraMap R A) (f 0)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
- map_zeroproof · cited by 1,614
- ContinuousStarstatement and proof · cited by 543
- IsTopologicalSemiringstatement and proof · cited by 442
Cited by4
Results whose statement or proof uses this declaration.
- CFC.sqrt_rpowproof · cited by 0
- CFC.sqrt_rpow_nnrealproof · cited by 0
- CFC.log_zeroproof · cited by 0
- CFC.zero_rpowproof · cited by 0