Theorems · Definition · Lie groups

NonUnitalSubsemiring.nonUnitalCommSemiringTopologicalClosure

{R : Type u_1} →
  [inst : TopologicalSpace R] →
    [inst_1 : NonUnitalSemiring R] →
      [inst_2 : IsSemitopologicalSemiring R] →
        [T2Space R] →
          (s : NonUnitalSubsemiring R) → (∀ (x y : ↥s), x * y = y * x) → NonUnitalCommSemiring ↥s.topologicalClosure

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

Defined in

Mathlib.Topology.Algebra.Ring.Basic

Cited by

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Foundations

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

Assumes

TopologicalSpaceNonUnitalSemiringIsSemitopologicalSemiringT2Space