Theorems · Theorem · general topology

BoundedContinuousFunction.extend_apply

∀ {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) (g : BoundedContinuousFunction α β)
  (h : BoundedContinuousFunction δ β) (x : α), (BoundedContinuousFunction.extend f g h) (f x) = g x

Defined in

Mathlib.Topology.ContinuousMap.Bounded.Basic

Cited by

1 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePseudoMetricSpaceTopologicalSpaceDiscreteTopology