Theorems · Theorem · functional analysis
StarSubalgebra.le_topologicalClosure
∀ {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] (s : StarSubalgebra R A), s ≤ s.topologicalClosure- Defined in
- Mathlib.Topology.Algebra.StarSubalgebra
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- subset_closureproof · cited by 309
- StarSubalgebrastatement and proof · cited by 194
- IsSemitopologicalSemiringstatement and proof · cited by 88
- StarSubalgebra.topologicalClosurestatement · cited by 22
Cited by6
Results whose statement or proof uses this declaration.
- StarAlgebra.elemental.self_memproof · cited by 7
- gelfandTransform_bijectiveproof · cited by 1
- StarAlgHomClass.ext_topologicalClosurestatement and proof · cited by 1
- StarAlgebra.elemental.starAlgHomClass_extproof · cited by 1
- StarAlgHom.ext_topologicalClosurestatement and proof · cited by 1
- StarSubalgebra.topologicalClosure_monoproof · cited by 0