Theorems · Theorem · functional analysis
Subalgebra.le_topologicalClosure
∀ {R : Type u_1} [inst : CommSemiring R] {A : Type u} [inst_1 : TopologicalSpace A] [inst_2 : Semiring A]
[inst_3 : Algebra R A] [inst_4 : IsSemitopologicalSemiring A] (s : Subalgebra R A), s ≤ s.topologicalClosure- Defined in
- Mathlib.Topology.Algebra.Algebra
- Cited by
- 4 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.
Cites8
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
- Subalgebrastatement and proof · cited by 1,353
- subset_closureproof · cited by 309
- IsSemitopologicalSemiringstatement and proof · cited by 88
- Subalgebra.topologicalClosurestatement · cited by 26
Cited by4
Results whose statement or proof uses this declaration.
- ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPointsproof · cited by 3
- ContinuousMap.inf_mem_subalgebra_closureproof · cited by 1
- Algebra.elemental.self_memproof · cited by 1
- ContinuousMap.sup_mem_subalgebra_closureproof · cited by 1