Theorems · Theorem · functional analysis
StarSubalgebra.topologicalClosure_coe
∀ {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.topologicalClosure = closure ↑s- Defined in
- Mathlib.Topology.Algebra.StarSubalgebra
- Cited by
- 1 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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 · cited by 8,199
- StarRingstatement and proof · cited by 1,686
- closurestatement · cited by 1,254
- StarModulestatement and proof · cited by 570
- ContinuousStarstatement and proof · cited by 543
- StarSubalgebrastatement and proof · cited by 194
- IsSemitopologicalSemiringstatement and proof · cited by 88
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMap.induction_on_of_compactproof · cited by 2