Theorems · Theorem · general topology

ContinuousWithinAt.prodMk

∀ {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} {g : α → γ} {s : Set α} {x : α},
  ContinuousWithinAt f s x → ContinuousWithinAt g s x → ContinuousWithinAt (fun x => (f x, g x)) s x

Defined in

Mathlib.Topology.ContinuousOn

Cited by

15 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace