instNonUnitalCommSemiringOfIsTopologicalSemiring

English

If β is NonUnitalCommSemiring and IsTopologicalSemiring, then C_c(α,β) becomes NonUnitalCommSemiring with pointwise addition and multiplication.

Русский

Если β — NonUnitalCommSemiring и IsTopologicalSemiring, то C_c(α,β) становится NonUnitalCommSemiring через точечное сложение и умножение.

LaTeX

$$$$ (f+g)(x) = f(x)+g(x), \ (f\cdot g)(x) = f(x)\cdot g(x) $$$$

Lean4

instance [NonUnitalCommSemiring β] [IsTopologicalSemiring β] : NonUnitalCommSemiring C_c(α, β) :=
  DFunLike.coe_injective.nonUnitalCommSemiring _ coe_zero coe_add coe_mul fun _ _ => rfl

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