English
There is a scalar tower structure relating 𝕜', 𝕜, and the space of bounded continuous functions: IsScalarTower 𝕜' 𝕜 (α →ᵇ β).
Русский
Существует структура стека скаляров между 𝕜', 𝕜 и пространством ограниченных непрерывных функций: IsScalarTower 𝕜' 𝕜 (α →ᵇ β).
LaTeX
$$$\text{IsScalarTower}(𝕜', 𝕜, α \to^{\mathrm{b}} β)$$$
Lean4
/-- The pointwise difference of two bounded continuous functions is again bounded continuous. -/
instance instSub : Sub (α →ᵇ R) where
sub f
g :=
{ toFun := fun x ↦ (f x - g x), map_bounded' := sub_bounded_of_bounded_of_bounded f.map_bounded' g.map_bounded' }