Theorems · Theorem · general topology
Topology.IsClosedEmbedding.isProperMap
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsClosedEmbedding f → IsProperMap fA closed embedding is proper.
- Defined in
- Mathlib.Topology.Maps.Proper.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
- Topology.IsEmbedding.injectiveproof · cited by 103
- IsProperMapstatement · cited by 66
- Topology.IsClosedEmbedding.toIsEmbeddingproof · cited by 27
- Topology.IsClosedEmbedding.continuousproof · cited by 25
- Topology.IsClosedEmbedding.isClosedMapproof · cited by 19
- isProperMap_of_isClosedMap_of_injproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- IsClosed.isProperMap_subtypeValproof · cited by 1
- properSMul_of_isClosedEmbeddingproof · cited by 0
- t2Space_of_properVAdd_of_t1AddGroupproof · cited by 0
- t2Space_of_properSMul_of_t1Groupproof · cited by 0
- properVAdd_of_isClosedEmbeddingproof · cited by 0
- PrespectralSpace.of_isClosedEmbeddingproof · cited by 0