Theorems · Theorem · general topology
Set.restrictPreimage_isClosedEmbedding
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} (s : Set β),
Topology.IsClosedEmbedding f → Topology.IsClosedEmbedding (s.restrictPreimage f)- Defined in
- Mathlib.Topology.LocalAtTarget
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 · cited by 7,166
- Set.preimagestatement · cited by 4,946
- Set.rangeproof · cited by 4,705
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
- Set.restrictPreimagestatement · cited by 84
- Topology.IsInducing.subtypeValproof · cited by 43
- Topology.IsClosedEmbedding.isClosed_rangeproof · cited by 41
- Topology.IsClosedEmbedding.toIsEmbeddingproof · cited by 27
- Set.range_restrictPreimageproof · cited by 8
- Topology.IsEmbedding.restrictPreimageproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.restrictPreimageproof · cited by 0