Theorems · Theorem · general topology

ContinuousMap.continuousOn_of_continuousOn_uncurry

∀ {X : Type u_2} {Y : Type u_3} {Z : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {s : Set X} (f : X → C(Y, Z)),
  ContinuousOn (Function.uncurry fun x y => (f x) y) (s ×ˢ Set.univ) → ContinuousOn f s

Defined in

Mathlib.Topology.CompactOpen

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace