Theorems · Theorem · general topology

UniformOnFun.comap_eq

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : UniformSpace β] {𝔖 : Set (Set α)} {f : γ → β},
  UniformOnFun.uniformSpace α γ 𝔖 = UniformSpace.comap (fun x => f ∘ x) (UniformOnFun.uniformSpace α β 𝔖)

If u is a uniform structure on β and f : γ → β, then 𝒱(α, γ, 𝔖, comap f u) = comap (fun g ↦ f ∘ g) 𝒱(α, γ, 𝔖, u₁).

Defined in

Mathlib.Topology.UniformSpace.UniformConvergenceTopology

Cited by

2 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpace