Theorems · Theorem · general topology
Homeomorph.isProperMap
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (e : X ≃ₜ Y), IsProperMap ⇑eA homeomorphism 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.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Homeomorphstatement and proof · cited by 725
- IsProperMapstatement · cited by 66
- Homeomorph.continuousproof · cited by 53
- Homeomorph.isClosedMapproof · cited by 18
- Homeomorph.injectiveproof · cited by 14
- isProperMap_of_isClosedMap_of_injproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- IsClosed.smul_left_of_isCompactproof · cited by 5
- IsClosed.vadd_left_of_isCompactproof · cited by 5
- isProperMap_fst_of_compactSpaceproof · cited by 3
- isProperMap_snd_of_compactSpaceproof · cited by 3
- ProperSMul.isProperMap_smul_pair_setproof · cited by 1
- ProperVAdd.isProperMap_vadd_pair_setproof · cited by 1