Theorems · Theorem · general topology

ContinuousAt.prodMap

∀ {X : Type u} {Y : Type v} {W : Type u_1} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] [inst_3 : TopologicalSpace W] {f : X → Z} {g : Y → W} {p : X × Y},
  ContinuousAt f p.1 → ContinuousAt g p.2 → ContinuousAt (Prod.map f g) p

Defined in

Mathlib.Topology.Constructions.SumProd

Cited by

5 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace