Theorems · Theorem · functional analysis
StarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer
∀ (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 : Algebra R A] [inst_5 : StarRing A] [inst_6 : StarModule R A]
[inst_7 : IsSemitopologicalSemiring A] [inst_8 : ContinuousStar A] [T2Space A] (s : Set A),
(StarAlgebra.adjoin R s).topologicalClosure ≤ StarSubalgebra.centralizer R ↑(StarSubalgebra.centralizer R s)- Defined in
- Mathlib.Topology.Algebra.StarSubalgebra
- Cited by
- 1 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- 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
- SetLike.coestatement and proof · cited by 8,199
- StarRingstatement and proof · cited by 1,686
- T2Spacestatement and proof · cited by 1,351
- Star.starproof · cited by 1,082
- StarModulestatement and proof · cited by 570
- ContinuousStarstatement and proof · cited by 543
- StarSubalgebrastatement · cited by 194
Cited by1
Results whose statement or proof uses this declaration.
- StarAlgebra.elemental.le_centralizer_centralizerproof · cited by 0