Theorems · Theorem · general topology

Topology.ContinuousMapGeneratedBy.ev_apply

∀ {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] [inst_3 : ∀ (i : ι), LocallyCompactSpace (X i)]
  [inst_4 : ∀ (i j : ι), Topology.IsGeneratedBy X (X i × X j)] (y : Y) (f : Topology.ContinuousMapGeneratedBy X Y Z),
  Topology.ContinuousMapGeneratedBy.ev (y, f) = f y

Defined in

Mathlib.Topology.Convenient.HomSpace

Cited by

0 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceLocallyCompactSpaceTopology.IsGeneratedBy