continuousMul — Mathlib

English

A subsemigroup S of a topological space M inherits a continuous multiplication from M; the subspace S with the induced topology is a topological semigroup.

Русский

Подпол semigroup S в топологическом пространстве M наследует непрерывное умножение от M; подпространство S с индуцированной топологией — топологический полугрупп.

LaTeX

$$instance continuousMul [TopologicalSpace M] [Semigroup M] [ContinuousMul M] (S : Subsemigroup M) : ContinuousMul S$$

Lean4

@[to_additive]
instance continuousMul [TopologicalSpace M] [Semigroup M] [ContinuousMul M] (S : Subsemigroup M) : ContinuousMul S :=
  IsInducing.continuousMul ({ toFun := (↑), map_mul' := fun _ _ => rfl } : MulHom S M) ⟨rfl⟩

Похожие утверждения