Theorems · Theorem · general topology

ContinuousMap.continuous_uncurry_of_continuous

∀ {X : Type u_2} {Y : Type u_3} {Z : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] [LocallyCompactSpace Y] (f : C(X, C(Y, Z))),
  Continuous (Function.uncurry fun x y => (f x) y)

The uncurried form of a continuous map X → C(Y, Z) is a continuous map X × Y → Z.

Defined in

Mathlib.Topology.CompactOpen

Cited by

3 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceLocallyCompactSpace