Theorems · Theorem · general topology

Isometry.comp_continuousOn_iff

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {f : α → β} {γ : Type u_3}
  [inst_2 : TopologicalSpace γ], Isometry f → ∀ {g : γ → α} {s : Set γ}, ContinuousOn (f ∘ g) s ↔ ContinuousOn g s

Defined in

Mathlib.Topology.MetricSpace.Isometry

Cited by

2 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpaceTopologicalSpace