Theorems · Theorem · Lie groups
Submonoid.topologicalClosure_minimal
∀ {M : Type u_3} [inst : TopologicalSpace M] [inst_1 : Monoid M] [inst_2 : SeparatelyContinuousMul M] (s : Submonoid M)
{t : Submonoid M}, s ≤ t → IsClosed ↑t → s.topologicalClosure ≤ t- Defined in
- Mathlib.Topology.Algebra.Monoid
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 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
- SetLike.coestatement and proof · cited by 8,199
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- IsClosedstatement and proof · cited by 1,639
- SeparatelyContinuousMulstatement and proof · cited by 133
- closure_minimalproof · cited by 94
- Submonoid.topologicalClosurestatement · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- topologicalClosure_subgroupClosure_toSubmonoidproof · cited by 1