Theorems · Theorem · functional analysis
cfc_apply_of_not_continuousOn
∀ {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} (a : A),
¬ContinuousOn f (spectrum R a) → cfc f a = 0- Cited by
- 10 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
- ContinuousOnstatement and proof · cited by 1,411
- ContinuousStarstatement and proof · cited by 543
- spectrumstatement and proof · cited by 510
- IsTopologicalSemiringstatement and proof · cited by 442
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- cfcstatement · cited by 228
Cited by10
Results whose statement or proof uses this declaration.
- cfc_congrproof · cited by 20
- cfc_casesproof · cited by 12
- cfc_starproof · cited by 3
- Unitization.cfcₙ_eq_cfc_inrproof · cited by 3
- SpectrumRestricts.cfc_eq_restrictproof · cited by 2
- cfc_negproof · cited by 2
- cfc_nonnegproof · cited by 2
- CFC.isUnit_rpow_iffproof · cited by 2
- cfc_apply_mkDproof · cited by 1
- cfc_nonposproof · cited by 0