Theorems · Theorem · general topology

ContinuousOn.comp_continuous

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

Defined in

Mathlib.Topology.ContinuousOn

Cited by

21 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace