Theorems · Theorem · functional analysis
NonUnitalSubalgebra.topologicalClosure_minimal
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : TopologicalSpace A] [inst_2 : NonUnitalSemiring A]
[inst_3 : Module R A] [inst_4 : ContinuousConstSMul R A] [inst_5 : IsSemitopologicalSemiring A]
{s t : NonUnitalSubalgebra R A}, s ≤ t → IsClosed ↑t → s.topologicalClosure ≤ t- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 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
- 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
- NonUnitalSemiringstatement and proof · cited by 339
- NonUnitalSubalgebrastatement and proof · cited by 215
- closure_minimalproof · cited by 94
- IsSemitopologicalSemiringstatement and proof · cited by 88
- NonUnitalSubalgebra.topologicalClosurestatement · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- NonUnitalSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizerproof · cited by 1
- NonUnitalAlgebra.elemental.le_of_memproof · cited by 1