instSup — Mathlib

English

The infimum and supremum in C_c(α,β) are taken pointwise: (f ∧ g)(x) = f(x) ∧ g(x) and (f ∨ g)(x) = f(x) ∨ g(x) whenever β has Inf/Sup. The respective complete lattices are inherited from β.

Русский

На C_c(α,β) операторы Inf/Sup берутся по точке: (f ∧ g)(x) = f(x) ∧ g(x), (f ∨ g)(x) = f(x) ∨ g(x).

LaTeX

$$Inf/ Sup in C_c(α,β) are defined pointwise using Inf/Sup in β.$$

Lean4

instance instSup : Max C_c(α, β) where
  max f
    g :=
    { toFun := f ⊔ g
      continuous_toFun := Continuous.sup f.continuous g.continuous
      hasCompactSupport' := f.hasCompactSupport.sup g.hasCompactSupport }

Похожие утверждения