Theorems · Definition · Lie groups
AddSubsemigroup.topologicalClosure
{M : Type u_3} →
[inst : TopologicalSpace M] →
[inst_1 : AddSemigroup M] → [SeparatelyContinuousAdd M] → AddSubsemigroup M → AddSubsemigroup MThe (topological-space) closure of an additive submonoid of a space M with
ContinuousAdd is itself an additive submonoid.
- Defined in
- Mathlib.Topology.Algebra.Monoid
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.coeproof · cited by 8,199
- closureproof · cited by 1,254
- AddSubsemigroupstatement and proof · cited by 262
- AddSemigroupstatement and proof · cited by 136
- SeparatelyContinuousAddstatement and proof · cited by 83
Cited by7
Results whose statement or proof uses this declaration.
- AddSubsemigroup.isClosed_topologicalClosurestatement · cited by 0
- AddSubmonoid.addCommMonoidTopologicalClosureproof · cited by 0
- AddSubsemigroup.le_topologicalClosurestatement · cited by 0
- AddSubsemigroup.topologicalClosure_minimalstatement · cited by 0
- AddSubsemigroup.coe_topologicalClosurestatement · cited by 0
- AddSubsemigroup.topologicalClosure_monostatement · cited by 0
- AddSubsemigroup.addCommSemigroupTopologicalClosurestatement and proof · cited by 0