Theorems · Theorem · functional analysis
SpectrumRestricts.of_subset_range_algebraMap
∀ {R : Type u_3} {S : Type u_4} {A : Type u_5} [inst : Semifield R] [inst_1 : Semifield S] [inst_2 : Ring A]
[inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] {a : A} {f : S → R},
Function.LeftInverse f ⇑(algebraMap R S) → spectrum S a ⊆ Set.range ⇑(algebraMap R S) → SpectrumRestricts a f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 47 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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- Set.rangestatement and proof · cited by 4,705
- map_zeroproof · cited by 1,614
- spectrumstatement and proof · cited by 510
- Semifieldstatement and proof · cited by 439
- quasispectrumproof · cited by 292
- SpectrumRestrictsstatement · cited by 51
Cited by1
Results whose statement or proof uses this declaration.
- SpectrumRestricts.nnreal_iffproof · cited by 8