Theorems · Theorem · general topology
Topology.IsQuotientMap.surjective
∀ {X : Type u_3} {Y : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsQuotientMap f → Function.Surjective f- Defined in
- Mathlib.Topology.Defs.Induced
- Cited by
- 24 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
- Topology.IsQuotientMapstatement and proof · cited by 124
Cited by24
Results whose statement or proof uses this declaration.
- IsAddQuotientCoveringMap.isCoveringMapproof · cited by 16
- IsQuotientCoveringMap.isCoveringMapproof · cited by 15
- Topology.IsQuotientMap.compproof · cited by 8
- Topology.IsQuotientMap.isStrictMap_iffproof · cited by 8
- AddMonoidHom.isOpenQuotientMap_of_isQuotientMapproof · cited by 3
- Topology.IsQuotientMap.of_compproof · cited by 3
- IsQuotientCoveringMap.monodromyPerm_injectiveproof · cited by 2
- TopologicalSpace.IsTopologicalBasis.isQuotientMapproof · cited by 2
- Topology.IsQuotientMap.of_comp_of_isCoinducingproof · cited by 2
- IsOpenQuotientMap.iff_isOpenMap_isQuotientMapproof · cited by 1
- Topology.IsQuotientMap.continuous_lift_prod_leftproof · cited by 1
- MonoidHom.isOpenQuotientMap_of_isQuotientMapproof · cited by 1