Theorems · Theorem · general topology
IsProperMap.isClosedMap
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsProperMap f → IsClosedMap fA proper map is closed.
- Defined in
- Mathlib.Topology.Maps.Proper.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsClosedMapstatement · cited by 138
- IsProperMapstatement and proof · cited by 66
- IsProperMap.clusterPt_of_mapClusterPtproof · cited by 4
- isClosedMap_iff_clusterPtproof · cited by 1
Cited by14
Results whose statement or proof uses this declaration.
- IsClosed.vadd_left_of_isCompactproof · cited by 5
- IsClosed.smul_left_of_isCompactproof · cited by 5
- isProperMap_iff_isClosedMap_and_compact_fibersproof · cited by 5
- IsProperMap.universally_closedproof · cited by 3
- IsProperMap.isClosed_rangeproof · cited by 2
- Polynomial.isClosedMap_evalproof · cited by 2
- IsProperMap.restrictPreimageproof · cited by 2
- isClosedMap_snd_of_compactSpaceproof · cited by 1
- isClosedMap_fst_of_compactSpaceproof · cited by 1
- isProperMap_iff_isClosedMap_of_injproof · cited by 1
- isClosedMap_distproof · cited by 0
- IsClosed.vadd_right_of_isCompactproof · cited by 0