Theorems · Theorem · functional analysis
Ideal.toCharacterSpace_apply_eq_zero_of_mem
∀ {A : Type u_1} [inst : NormedCommRing A] [inst_1 : NormedAlgebra ℂ A] [inst_2 : CompleteSpace A] (I : Ideal A)
[inst_3 : I.IsMaximal] {a : A}, a ∈ I → I.toCharacterSpace a = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 299 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 and proof · cited by 62,936
- Set.Elemstatement · cited by 7,166
- Complexstatement and proof · cited by 5,565
- Idealstatement and proof · cited by 4,748
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- Ideal.Quotient.mkproof · cited by 610
- spectrumproof · cited by 510
- Ideal.IsMaximalstatement and proof · cited by 452
- NormedCommRingstatement and proof · cited by 218
- WeakDualstatement · cited by 103
- Ideal.Quotient.eq_zero_iff_memproof · cited by 74
Cited by1
Results whose statement or proof uses this declaration.
- WeakDual.CharacterSpace.exists_apply_eq_zeroproof · cited by 1