Theorems · Theorem · general topology
Set.restrictPreimage_isOpenEmbedding
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} (s : Set β),
Topology.IsOpenEmbedding f → Topology.IsOpenEmbedding (s.restrictPreimage f)- Defined in
- Mathlib.Topology.LocalAtTarget
- Cited by
- 2 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.IsOpenEmbeddingstatement and proof · cited by 231
- continuous_subtype_valproof · cited by 159
- Set.restrictPreimagestatement · cited by 84
- Topology.IsOpenEmbedding.toIsEmbeddingproof · cited by 61
- Continuous.isOpen_preimageproof · cited by 51
- Topology.IsOpenEmbedding.isOpen_rangeproof · cited by 33
- Set.range_restrictPreimageproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2
- Topology.IsOpenEmbedding.restrictPreimageproof · cited by 1