Theorems · Theorem · general topology

EMetric.uniformContinuousOn_iff

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

ε-δ characterization of uniform continuity on a set for pseudoemetric spaces

Defined in

Mathlib.Topology.EMetricSpace.Defs

Cited by

1 results in Mathlib

Foundations

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

Assumes

PseudoEMetricSpacePseudoEMetricSpace