Theorems · Theorem · general topology

ContinuousOn.comp

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  [inst_2 : TopologicalSpace γ] {f : α → β} {s : Set α} {g : β → γ} {t : Set β},
  ContinuousOn g t → ContinuousOn f s → Set.MapsTo f s t → ContinuousOn (g ∘ f) s

See also ContinuousOn.comp' using the form fun y ↦ g (f y) instead of g ∘ f.

Defined in

Mathlib.Topology.ContinuousOn

Cited by

73 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace