Theorems · Theorem · general topology

EMetric.uniformContinuous_iff

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

ε-δ characterization of uniform continuity on pseudoemetric spaces

Defined in

Mathlib.Topology.EMetricSpace.Defs

Cited by

3 results in Mathlib

Foundations

Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace