Theorems · Theorem · general topology
Topology.IsQuotientMap.continuous
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsQuotientMap f → Continuous f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 14 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.
Cites5
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
- Continuousstatement · cited by 2,592
- continuous_idproof · cited by 192
- Topology.IsQuotientMapstatement and proof · cited by 124
- Topology.IsQuotientMap.continuous_iffproof · cited by 10
Cited by14
Results whose statement or proof uses this declaration.
- ConnectedComponents.continuous_coeproof · cited by 3
- IsQuotientCoveringMap.monodromy_toPermFiberproof · cited by 3
- AddMonoidHom.isOpenQuotientMap_of_isQuotientMapproof · cited by 3
- IsQuotientCoveringMap.monodromyPerm_injectiveproof · cited by 2
- DiscreteQuotient.proj_continuousproof · cited by 2
- TopologicalSpace.IsTopologicalBasis.isQuotientMapproof · cited by 2
- IsQuotientCoveringMap.ker_monodromyPermstatement and proof · cited by 2
- MonoidHom.isOpenQuotientMap_of_isQuotientMapproof · cited by 1
- IsOpenQuotientMap.iff_isOpenMap_isQuotientMapproof · cited by 1
- IsQuotientCoveringMap.fundamentalGroupToMulOpposite_surjectiveproof · cited by 1
- Topology.IsQuotientMap.separableSpaceproof · cited by 0
- IsAddQuotientCoveringMap.ker_monodromyPermstatement · cited by 0