Theorems · Theorem · general topology
TopologicalSpace.generatedBy_eq_coinduced
∀ {ι : Type t} (X : ι → Type u) [inst : (i : ι) → TopologicalSpace (X i)] {Y : Type v} [tY : TopologicalSpace Y],
TopologicalSpace.generatedBy X = TopologicalSpace.coinduced (fun x => x.fst.snd x.snd) inferInstanceThe X-generated topology is also coinduced by a single map out of a sigma type.
- Defined in
- Mathlib.Topology.Convenient.GeneratedBy
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousMapstatement and proof · cited by 2,491
- iSupproof · cited by 2,415
- TopologicalSpace.coinducedstatement and proof · cited by 56
- TopologicalSpace.generatedBystatement · cited by 12
- iSup_sigmaproof · cited by 5
- coinduced_iSupproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- deltaGenerated_eq_coinducedproof · cited by 0