Theorems · Theorem · functional analysis
StarAlgebra.elemental.self_mem
∀ (R : Type u_1) {A : Type u_2} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : TopologicalSpace A]
[inst_3 : Semiring A] [inst_4 : StarRing A] [inst_5 : IsSemitopologicalSemiring A] [inst_6 : ContinuousStar A]
[inst_7 : Algebra R A] [inst_8 : StarModule R A] (x : A), x ∈ StarAlgebra.elemental R x- Defined in
- Mathlib.Topology.Algebra.StarSubalgebra
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 88 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
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- StarRingstatement and proof · cited by 1,686
- StarModulestatement and proof · cited by 570
- ContinuousStarstatement and proof · cited by 543
- StarSubalgebrastatement · cited by 194
- IsSemitopologicalSemiringstatement and proof · cited by 88
- StarAlgebra.adjoinproof · cited by 42
- StarAlgebra.elementalstatement · cited by 26
- StarSubalgebra.le_topologicalClosureproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- StarAlgebra.elemental.starAlgHomClass_extstatement and proof · cited by 1
- StarAlgebra.elemental.star_self_memproof · cited by 1
- continuousFunctionalCalculus_map_idstatement · cited by 1
- StarAlgebra.elemental.continuous_characterSpaceToSpectrumproof · cited by 0
- StarAlgebra.elemental.induction_onstatement and proof · cited by 0
- StarAlgebra.elemental.le_iff_memproof · cited by 0
- StarAlgebra.elemental.bijective_characterSpaceToSpectrumproof · cited by 0