Theorems · Theorem · general topology

UniformOnFun.edist_continuousRestrict

∀ {α : Type u_1} {β : Type u_2} {𝔖 : Set (Set α)} [inst : Finite ↑𝔖] [inst_1 : PseudoMetricSpace β]
  [inst_2 : TopologicalSpace α] {f g : UniformOnFun α β 𝔖} [inst_3 : CompactSpace ↑(⋃₀ 𝔖)]
  (hf : ContinuousOn ((UniformOnFun.toFun 𝔖) f) (⋃₀ 𝔖)) (hg : ContinuousOn ((UniformOnFun.toFun 𝔖) g) (⋃₀ 𝔖)),
  edist { toFun := (⋃₀ 𝔖).domRestrict ((UniformOnFun.toFun 𝔖) f), continuous_toFun := ⋯ }
      { toFun := (⋃₀ 𝔖).domRestrict ((UniformOnFun.toFun 𝔖) g), continuous_toFun := ⋯ } =
    edist f g

Defined in

Mathlib.Topology.MetricSpace.UniformConvergence

Cited by

0 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FinitePseudoMetricSpaceTopologicalSpaceCompactSpace