instSemigroupWithZeroOfContinuousMul

English

With ContinuousMul on β, the structure SemigroupWithZero on C_c(α, β) exists, defined by pointwise multiplication with the zero element as the absorbing element.

Русский

При наличии ContinuousMul на β существует структура SemigroupWithZero на C_c(α, β), заданная точечно умножением и нулём как поглотителем.

LaTeX

$$$ \text{[SemigroupWithZero β]} \Rightarrow \text{SemigroupWithZero } C_c(α, β) $$$

Lean4

instance [SemigroupWithZero β] [ContinuousMul β] : SemigroupWithZero C_c(α, β) :=
  DFunLike.coe_injective.semigroupWithZero _ coe_zero coe_mul

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