Theorems · Theorem · functional analysis
NonUnitalStarSubalgebra.topologicalClosure_minimal
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : TopologicalSpace A] [inst_2 : Star A]
[inst_3 : NonUnitalSemiring A] [inst_4 : Module R A] [inst_5 : ContinuousStar A] [inst_6 : ContinuousConstSMul R A]
[inst_7 : IsSemitopologicalSemiring A] (s : NonUnitalStarSubalgebra R A) {t : NonUnitalStarSubalgebra R A},
s ≤ t → IsClosed ↑t → s.topologicalClosure ≤ t- Cited by
- 3 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- IsClosedstatement and proof · cited by 1,639
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousStarstatement and proof · cited by 543
- Starstatement and proof · cited by 496
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalStarSubalgebrastatement and proof · cited by 196
- closure_minimalproof · cited by 94
- IsSemitopologicalSemiringstatement and proof · cited by 88
Cited by3
Results whose statement or proof uses this declaration.
- NonUnitalStarAlgebra.elemental.le_of_memproof · cited by 1
- cfcₙ_memproof · cited by 0