Theorems · Theorem · general topology

UniformFun.comap_eq

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

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

Defined in

Mathlib.Topology.UniformSpace.UniformConvergenceTopology

Cited by

2 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

UniformSpace