Theorems · Theorem · general topology
IsClosedMap.isClosed_range
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
IsClosedMap f → IsClosed (Set.range f)- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.rangestatement · cited by 4,705
- Set.univproof · cited by 3,945
- IsClosedstatement · cited by 1,639
- Set.image_univproof · cited by 322
- IsClosedMapstatement and proof · cited by 138
- isClosed_univproof · cited by 43
Cited by12
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.compproof · cited by 14
- IsProperMap.isClosed_rangeproof · cited by 2
- Irrational.eventually_forall_le_dist_cast_divproof · cited by 2
- Topology.IsClosedEmbedding.idproof · cited by 1
- AlgebraicGeometry.IsSeparated.of_valuativeCriterionproof · cited by 1
- AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPointsproof · cited by 1
- MeasureTheory.measurableEquiv_range_coe_nat_of_infinite_of_countableproof · cited by 1
- ProfiniteGrp.toLimit_surjectiveproof · cited by 0
- isClosed_range_sigmaMkproof · cited by 0
- Valued.exists_coe_eq_vproof · cited by 0