Theorems · Theorem · general topology

continuousWithinAt_prod_of_discrete_right

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  [inst_2 : TopologicalSpace γ] [DiscreteTopology β] {f : α × β → γ} {s : Set (α × β)} {x : α × β},
  ContinuousWithinAt f s x ↔ ContinuousWithinAt (fun x_1 => f (x_1, x.2)) {a | (a, x.2) ∈ s} x.1

Defined in

Mathlib.Topology.ContinuousOn

Cited by

1 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceDiscreteTopology