Theorems · Definition · general topology

Topology.ContinuousMapGeneratedBy.ev

{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] →
              [∀ (i : ι), LocallyCompactSpace (X i)] →
                [∀ (i j : ι), Topology.IsGeneratedBy X (X i × X j)] →
                  Topology.ContinuousMapGeneratedBy X (Y × Topology.ContinuousMapGeneratedBy X Y Z) Z

The evaluation Y × ContinuousMapGeneratedBy X Y Z → Z as a X-continuous map.

Defined in

Mathlib.Topology.Convenient.HomSpace

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceLocallyCompactSpaceTopology.IsGeneratedBy