Theorems · Definition · Lie groups

AddSubmonoid.addCommMonoidTopologicalClosure

{M : Type u_3} →
  [inst : TopologicalSpace M] →
    [inst_1 : AddMonoid M] →
      [inst_2 : SeparatelyContinuousAdd M] →
        [T2Space M] → (s : AddSubmonoid M) → (∀ (x y : ↥s), x + y = y + x) → AddCommMonoid ↥s.topologicalClosure

If a submonoid of an additive topological monoid is commutative, then so is its topological closure. See note [reducible non-instances].

Defined in

Mathlib.Topology.Algebra.Monoid

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddMonoidSeparatelyContinuousAddT2Space