Theorems · Theorem · general topology
IsOpenQuotientMap.isOpenMap
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsOpenQuotientMap f → IsOpenMap fAn open quotient map is an open map.
- Defined in
- Mathlib.Topology.Defs.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- IsOpenMapstatement · cited by 253
- 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
- IsOpenQuotientMap.map_nhds_eqproof · cited by 3
- coinduced_eq_induced_of_isOpenQuotientMap_of_isInducingproof · cited by 2
- Complex.isOpenQuotientMap_pow_compl_zeroproof · cited by 1
- IsOpenQuotientMap.iff_isOpenMap_isQuotientMapproof · cited by 1
- IsOpenQuotientMap.isOpenMap_iffproof · cited by 1
- IsModuleTopology.isOpenMap_of_surjectiveₛₗproof · cited by 1
- IsOpenQuotientMap.of_compproof · cited by 1
- IsOpenQuotientMap.restrictPreimageproof · cited by 1