Theorems · Theorem · general topology
Topology.isStrictMap_iff_isQuotientMap_rangeFactorization
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsStrictMap f ↔ Topology.IsQuotientMap (Set.rangeFactorization f)- Defined in
- Mathlib.Topology.Maps.Strict.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- Topology.IsQuotientMapstatement · cited by 124
- Set.rangeFactorizationstatement · cited by 56
- Topology.IsStrictMapstatement · cited by 45
Cited by5
Results whose statement or proof uses this declaration.
- IsOpenMap.isStrictMapproof · cited by 2
- IsClosedMap.isStrictMapproof · cited by 1
- Topology.IsStrictMap.continuousproof · cited by 0
- ContinuousLinearMap.isStrictMap_of_finiteDimensionalproof · cited by 0
- Topology.isQuotientMap_iff_isStrictMap_surjectiveproof · cited by 0