Theorems · Definition · Lie groups

Subring.commRingTopologicalClosure

{R : Type u_1} →
  [inst : TopologicalSpace R] →
    [inst_1 : Ring R] →
      [inst_2 : IsSemitopologicalRing R] →
        [T2Space R] → (s : Subring R) → (∀ (x y : ↥s), x * y = y * x) → CommRing ↥s.topologicalClosure

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

Defined in

Mathlib.Topology.Algebra.Ring.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceRingIsSemitopologicalRingT2Space