Theorems · Theorem · general topology

continuousWithinAt_prod_of_discrete_left

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

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