Theorems · Theorem · general topology

Metric.uniformContinuous_iff

∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {f : α → β},
  UniformContinuous f ↔ ∀ ε > 0, ∃ δ > 0, ∀ ⦃a b : α⦄, dist a b < δ → dist (f a) (f b) < ε

Defined in

Mathlib.Topology.MetricSpace.Pseudo.Defs

Cited by

13 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpacePseudoMetricSpace