Theorems · Theorem · general topology

continuous_iff_continuous_dist

∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : TopologicalSpace β] {f : β → α},
  Continuous f ↔ Continuous fun x => dist (f x.1) (f x.2)

Defined in

Mathlib.Topology.MetricSpace.Pseudo.Constructions

Cited by

1 results in Mathlib

Foundations

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

Assumes

PseudoMetricSpaceTopologicalSpace