English
For T2 spaces, the elemental algebra inherits a nonunital commutative semiring structure on its subtype of elements.
Русский
Для пространств T2 элементарная алгебра наследует немодулярную коммутативную полускольную структуру на своем подтипе элементов.
LaTeX
$$NonUnitalCommSemiring (Subtype fun x => Mem (elemental R x).topologicalClosure x)$$
Lean4
instance [T2Space A] {x : A} : NonUnitalCommSemiring (elemental R x) :=
nonUnitalCommSemiringTopologicalClosure _
letI : NonUnitalCommSemiring (adjoin R { x }) :=
NonUnitalAlgebra.adjoinNonUnitalCommSemiringOfComm R fun y hy z hz =>
by
rw [Set.mem_singleton_iff] at hy hz
rw [hy, hz]
fun _ _ => mul_comm _ _
