Theorems · Theorem · functional analysis
Subalgebra.topologicalClosure_star_comm
∀ {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] [ContinuousStar A] (s : Subalgebra R A),
(star s).topologicalClosure = star s.topologicalClosure- Defined in
- Mathlib.Topology.Algebra.StarSubalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites20
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
- le_antisymmproof · cited by 2,068
- StarRingstatement and proof · cited by 1,686
- Subalgebrastatement and proof · cited by 1,353
- Star.starstatement and proof · cited by 1,082
- StarModulestatement and proof · cited by 570
- ContinuousStarstatement and proof · cited by 543
- subset_closureproof · cited by 309
- isClosed_closureproof · cited by 195
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