Theorems · Theorem · general topology
Topology.isStrictMap_iff_isHomeomorph_quotientKerEquivRange
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsStrictMap f ↔ IsHomeomorph ⇑(Setoid.quotientKerEquivRange f)A map is a strict map if and only if the canonical bijection
Quotient (Setoid.ker f) ≃ Set.range f is a homeomorphism.
- Defined in
- Mathlib.Topology.Maps.Strict.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- Topology.IsQuotientMapproof · cited by 124
- IsHomeomorphstatement · cited by 69
- Set.rangeFactorizationproof · cited by 56
- Topology.IsStrictMapstatement · cited by 45
- Setoid.kerstatement · cited by 43
- isQuotientMap_quotient_mk'proof · cited by 16
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.