Theorems · Definition · general topology

ContinuousMap.uncurry

{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] → C(X, C(Y, Z)) → C(X × Y, Z)

The uncurried form of a continuous map X → C(Y, Z) as a continuous map X × Y → Z (if Y is locally compact). If X is also locally compact, then this is a homeomorphism between the two function spaces, see Homeomorph.curry.

Defined in

Mathlib.Topology.CompactOpen

Cited by

5 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceLocallyCompactSpace