Theorems · Definition · category theory

ContinuousGeneratedByCat.Hom.hom

{ι : Type t} →
  {X : ι → Type u} →
    [inst : (i : ι) → TopologicalSpace (X i)] →
      {Y Z : ContinuousGeneratedByCat X} → Y.Hom Z → Topology.ContinuousMapGeneratedBy X ↑Y ↑Z

the underlying X-continuous map of a morphism in ContinuousGeneratedByCat X.

Defined in: Mathlib.Topology.Convenient.Category
Cited by: 3 results in Mathlib
Foundations: Depth 4 from the axioms · uses no axioms
Assumes: TopologicalSpace

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Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopologicalSpacestatement and proof · cited by 24,529
Topology.ContinuousMapGeneratedBystatement · cited by 28
ContinuousGeneratedByCatstatement and proof · cited by 23
ContinuousGeneratedByCat.carrierstatement · cited by 14
ContinuousGeneratedByCat.Homstatement and proof · cited by 3

Cited by3

Results whose statement or proof uses this declaration.

ContinuousGeneratedByCat.homMk_hom_applystatement and proof · cited by 0
ContinuousGeneratedByCat.forget₂_map_hom_applystatement and proof · cited by 0
ContinuousGeneratedByCat.fromGeneratedByTopCat_map_hom_applystatement and proof · cited by 0