nonUnitalCommSemiringTopologicalClosure

English

If a non-unital star subalgebra is commutative, then its topological closure is a non-unital commutative semiring.

Русский

Если неполная звёздная подсхема коммутативна, то её топологическое замыкание тоже образует неполуподмножество коммутативного полускольного кольца.

LaTeX

$$$s.topologicalClosure \in \mathrm{NonUnitalCommSemiring}(s.topologicalClosure)$$$

Lean4

/-- If a non-unital star subalgebra of a non-unital topological star algebra is commutative, then
so is its topological closure.

See note [reducible non-instances] -/
abbrev nonUnitalCommSemiringTopologicalClosure [T2Space A] (s : NonUnitalStarSubalgebra R A)
    (hs : ∀ x y : s, x * y = y * x) : NonUnitalCommSemiring s.topologicalClosure :=
  s.toNonUnitalSubalgebra.nonUnitalCommSemiringTopologicalClosure hs

Похожие утверждения