Theorems · Definition · Lie groups

Subgroup.commGroupTopologicalClosure

{G : Type w} →
  [inst : TopologicalSpace G] →
    [inst_1 : Group G] →
      [inst_2 : IsTopologicalGroup G] →
        [T2Space G] → (s : Subgroup G) → (∀ (x y : ↥s), x * y = y * x) → CommGroup ↥s.topologicalClosure

If a subgroup of a topological group is commutative, then so is its topological closure. See note [reducible non-instances].

Defined in

Mathlib.Topology.Algebra.Group.Basic

Cited by

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Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceGroupIsTopologicalGroupT2Space