Theorems · Definition · Lie groups

Subsemigroup.commSemigroupTopologicalClosure

{M : Type u_3} →
  [inst : TopologicalSpace M] →
    [inst_1 : Semigroup M] →
      [inst_2 : SeparatelyContinuousMul M] →
        [T2Space M] → (s : Subsemigroup M) → (∀ (x y : ↥s), x * y = y * x) → CommSemigroup ↥s.topologicalClosure

If a subsemigroup of a topological semigroup 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 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceSemigroupSeparatelyContinuousMulT2Space