Theorems · Theorem · general topology
IsOpenQuotientMap.surjective
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsOpenQuotientMap f → Function.Surjective fAn open quotient map is surjective.
- Defined in
- Mathlib.Topology.Defs.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
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
- IsOpenQuotientMapstatement and proof · cited by 65
Cited by16
Results whose statement or proof uses this declaration.
- IsOpenQuotientMap.isQuotientMapproof · cited by 12
- IsOpenQuotientMap.compproof · cited by 5
- IsOpenQuotientMap.prodMapproof · cited by 4
- IsOpenQuotientMap.dense_preimage_iffproof · cited by 3
- coinduced_eq_induced_of_isOpenQuotientMap_of_isInducingproof · cited by 2
- Complex.isOpenQuotientMap_pow_compl_zeroproof · cited by 1
- IsOpenQuotientMap.isOpenMap_iffproof · cited by 1
- IsOpenQuotientMap.of_compproof · cited by 1
- IsOpenQuotientMap.restrictPreimageproof · cited by 1
- t2Space_iff_of_isOpenQuotientMapproof · cited by 0
- TopologicalGroup.IsSES.inducedMeasure_lt_of_injOnproof · cited by 0
- IsOpenQuotientMap.locallyCompactSpaceproof · cited by 0