Theorems · Definition · general topology

Topology.IsGeneratedBy.homeomorph

{ι : Type t} →
  {X : ι → Type u} →
    [inst : (i : ι) → TopologicalSpace (X i)] →
      {Y : Type v} →
        [tY : TopologicalSpace Y] → [Topology.IsGeneratedBy X Y] → Topology.WithGeneratedByTopology X Y ≃ₜ Y

The homeomorphism WithGeneratedByTopology X Y ≃ₜ Y when Y is X-generated.

Defined in: Mathlib.Topology.Convenient.GeneratedBy
Cited by: 6 results in Mathlib
Foundations: Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace Topology.IsGeneratedBy

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites6

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
Equivproof · cited by 8,337
Homeomorphstatement · cited by 725
Topology.IsGeneratedBystatement and proof · cited by 38
Topology.WithGeneratedByTopologystatement and proof · cited by 25
Topology.WithGeneratedByTopology.equivproof · cited by 24

Cited by8

Results whose statement or proof uses this declaration.

Topology.IsGeneratedBy.continuous_iffproof · cited by 3
Topology.IsGeneratedBy.isOpen_iffproof · cited by 2
Topology.IsGeneratedBy.isClosed_iffproof · cited by 1
ContinuousGeneratedByCat.equivalenceUnitIsoproof · cited by 1
Topology.IsGeneratedBy.homeomorph.congr_simpstatement and proof · cited by 0
Topology.IsGeneratedBy.homeomorph_coestatement · cited by 0
Topology.IsGeneratedBy.homeomorph_symm_coestatement · cited by 0
ContinuousGeneratedByCat.equivalenceFunctorIsoproof · cited by 0