Theorems · Definition · general topology

Topology.ContinuousMapGeneratedBy.curryEquiv

{ι : Type t} →
  {X : ι → Type u} →
    [inst : (i : ι) → TopologicalSpace (X i)] →
      {Y : Type v} →
        [inst_1 : TopologicalSpace Y] →
          {Z : Type v'} →
            [inst_2 : TopologicalSpace Z] →
              {T : Type v''} →
                [inst_3 : TopologicalSpace T] →
                  [∀ (i : ι), LocallyCompactSpace (X i)] →
                    [∀ (i j : ι), Topology.IsGeneratedBy X (X i × X j)] →
                      Topology.ContinuousMapGeneratedBy X (Y × Z) T ≃
                        Topology.ContinuousMapGeneratedBy X Z (Topology.ContinuousMapGeneratedBy X Y T)

The bijection between the type of X-continuous maps Y × Z → T and the type of X-continuous maps Z → ContinuousMapGeneratedBy X Y T.

Defined in

Mathlib.Topology.Convenient.HomSpace

Cited by

2 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceLocallyCompactSpaceTopology.IsGeneratedBy