Theorems · Theorem · general topology

ContinuousMap.continuous_mkD_of_uncurry

∀ {X : Type u_2} {Y : Type u_3} {T : Type u_5} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace T] (f : T → X → Y) (g : C(X, Y)),
  Continuous (Function.uncurry f) → Continuous fun x => ContinuousMap.mkD (f x) g

A variant of ContinuousMap.continuous_of_continuous_uncurry in terms of ContinuousMap.mkD. Of course, in this particular setting, fun x ↦ mkD (f x) g is just f, but the mkD spelling appears naturally in the context of C(α, β)-valued integration.

Defined in

Mathlib.Topology.CompactOpen

Cited by

1 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace