Theorems · Theorem · general topology

BoundedContinuousFunction.dist_lt_of_nonempty_compact

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

Defined in

Mathlib.Topology.ContinuousMap.Bounded.Basic

Cited by

2 results in Mathlib

Foundations

Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePseudoMetricSpaceNonemptyCompactSpace