Theorems · Theorem · general topology
IsProperMap.restrictPreimage
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
IsProperMap f → ∀ (s : Set β), IsProperMap (s.restrictPreimage f)- Defined in
- Mathlib.Topology.LocalAtTarget
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- Set.preimagestatement and proof · cited by 4,946
- IsCompactproof · cited by 1,282
- Set.image_singletonproof · cited by 174
- Set.restrictPreimagestatement · cited by 84
- IsProperMapstatement and proof · cited by 66
- Topology.IsEmbedding.subtypeValproof · cited by 41
- isCompact_singletonproof · cited by 32
- Topology.IsEmbedding.isCompact_iffproof · cited by 17
- IsProperMap.isClosedMapproof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- ProperSMul.isProperMap_smul_pair_setproof · cited by 1
- ProperVAdd.isProperMap_vadd_pair_setproof · cited by 1