Theorems · Theorem · general topology

Metric.uniformContinuousOn_iff_le

∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {f : α → β} {s : Set α},
  UniformContinuousOn f s ↔ ∀ ε > 0, ∃ δ > 0, ∀ x ∈ s, ∀ y ∈ s, dist x y ≤ δ → dist (f x) (f y) ≤ ε

Defined in

Mathlib.Topology.MetricSpace.Pseudo.Defs

Cited by

2 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpacePseudoMetricSpace