Theorems · Theorem · general topology

ContinuousWithinAt.comp_of_mem_nhdsWithin_image_of_eq

∀ {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} {y : β},
  ContinuousWithinAt g t y →
    ContinuousWithinAt f s x → t ∈ nhdsWithin y (f '' s) → f x = y → ContinuousWithinAt (g ∘ f) s x

Defined in

Mathlib.Topology.ContinuousOn

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace