Theorems · Theorem · general topology
Topology.IsInducing.isClosedMap
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
Topology.IsInducing f → IsClosed (Set.range f) → IsClosedMap f- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- IsClosedstatement and proof · cited by 1,639
- Topology.IsInducingstatement and proof · cited by 266
- IsClosedMapstatement · cited by 138
- Set.image_preimage_eq_inter_rangeproof · cited by 121
- IsClosed.interproof · cited by 61
- Topology.IsInducing.isClosed_iffproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.isClosedMapproof · cited by 19
- SeparationQuotient.isClosedMap_mkproof · cited by 1