Theorems · Definition · general topology
DiscreteQuotient.toSetoid
{X : Type u_5} → [inst : TopologicalSpace X] → DiscreteQuotient X → Setoid XThe setoid whose quotient yields the discrete quotient.
- Defined in
- Mathlib.Topology.DiscreteQuotient
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- DiscreteQuotientstatement and proof · cited by 65
Cited by52
Results whose statement or proof uses this declaration.
- DiscreteQuotient.projstatement · cited by 23
- DiscreteQuotient.ofLEstatement · cited by 14
- DiscreteQuotient.mapstatement · cited by 9
- DiscreteQuotient.proj_surjectivestatement · cited by 4
- DiscreteQuotient.comapproof · cited by 3
- DiscreteQuotient.finsetClopensproof · cited by 3
- DiscreteQuotient.isClopen_preimagestatement and proof · cited by 3
- LocallyConstant.liftstatement and proof · cited by 2
- Profinite.exists_locallyConstantproof · cited by 2
- DiscreteQuotient.fiber_eqstatement · cited by 2
- DiscreteQuotient.ofLE_projstatement · cited by 2
- DiscreteQuotient.proj_continuousstatement · cited by 2