Theorems · Theorem · functional analysis
Subalgebra.topologicalClosure_adjoin_le_centralizer_centralizer
∀ (R : Type u_1) [inst : CommSemiring R] {A : Type u} [inst_1 : TopologicalSpace A] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : IsSemitopologicalSemiring A] [T2Space A] (s : Set A),
(Algebra.adjoin R s).topologicalClosure ≤ Subalgebra.centralizer R ↑(Subalgebra.centralizer R s)- Defined in
- Mathlib.Topology.Algebra.Algebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Subalgebrastatement · cited by 1,353
- T2Spacestatement and proof · cited by 1,351
- Algebra.adjoinstatement · cited by 535
- IsSemitopologicalSemiringstatement and proof · cited by 88
- Subalgebra.topologicalClosurestatement · cited by 26
- Subalgebra.centralizerstatement and proof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.elemental.le_centralizer_centralizerproof · cited by 0