Theorems · Theorem · functional analysis
Subalgebra.isClosed_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), IsClosed ↑s.topologicalClosure- Defined in
- Mathlib.Topology.Algebra.Algebra
- Cited by
- 1 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · 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 and proof · cited by 8,199
- IsClosedstatement and proof · cited by 1,639
- Subalgebrastatement and proof · cited by 1,353
- closureproof · cited by 1,254
- isClosed_closureproof · cited by 195
- IsSemitopologicalSemiringstatement and proof · cited by 88
- Subalgebra.topologicalClosurestatement and proof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPointsproof · cited by 3