Theorems · Theorem · general topology
isSeparatedMap_iff_isClosed_diagonal
∀ {X : Type u_1} {Y : Sort u_2} [inst : TopologicalSpace X] {f : X → Y},
IsSeparatedMap f ↔ IsClosed (Function.pullbackDiagonal f)- Defined in
- Mathlib.Topology.SeparatedMap
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- Compl.complproof · cited by 2,925
- Disjointproof · cited by 2,201
- SProd.sprodproof · cited by 1,750
- IsClosedstatement and proof · cited by 1,639
- Filter.comapproof · cited by 546
- Set.disjoint_leftproof · cited by 121
- nhds_prod_eqproof · cited by 84
- subset_rflproof · cited by 77
Cited by4
Results whose statement or proof uses this declaration.
- isSeparatedMap_iff_isClosedEmbeddingproof · cited by 1
- IsSeparatedMap.isClosed_eqLocusproof · cited by 1
- IsSeparatedMap.pullbackproof · cited by 0
- IsSeparatedMap.comp_rightproof · cited by 0