Theorems · Theorem · general topology

BoundedContinuousFunction.dist_extend_extend

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β] {δ : Type u_2}
  [inst_2 : TopologicalSpace δ] [inst_3 : DiscreteTopology δ] (f : α ↪ δ) (g₁ g₂ : BoundedContinuousFunction α β)
  (h₁ h₂ : BoundedContinuousFunction δ β),
  dist (BoundedContinuousFunction.extend f g₁ h₁) (BoundedContinuousFunction.extend f g₂ h₂) =
    max (dist g₁ g₂) (dist (h₁.domRestrict (Set.range ⇑f)ᶜ) (h₂.domRestrict (Set.range ⇑f)ᶜ))

Defined in

Mathlib.Topology.ContinuousMap.Bounded.Basic

Cited by

1 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePseudoMetricSpaceTopologicalSpaceDiscreteTopology