Theorems · Theorem · general topology

ContinuousWithinAt.comp_of_mem_nhdsWithin_image

∀ {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} {x : α} {g : β → γ} {t : Set β},
  ContinuousWithinAt g t (f x) →
    ContinuousWithinAt f s x → t ∈ nhdsWithin (f x) (f '' s) → ContinuousWithinAt (g ∘ f) s x

Defined in

Mathlib.Topology.ContinuousOn

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace