Theorems · Theorem · general topology

BoundedContinuousFunction.dist_lt_iff_of_compact

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : PseudoMetricSpace β]
  {f g : BoundedContinuousFunction α β} {C : ℝ} [CompactSpace α],
  0 < C → (dist f g < C ↔ ∀ (x : α), dist (f x) (g x) < C)

Defined in

Mathlib.Topology.ContinuousMap.Bounded.Basic

Cited by

2 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePseudoMetricSpaceCompactSpace