Theorems · Theorem · algebraic geometry
Topology.IsLocallyConstructible.preimage_of_isOpenEmbedding
∀ {X : Type u_2} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set Y},
Topology.IsLocallyConstructible s → Topology.IsOpenEmbedding f → Topology.IsLocallyConstructible (f ⁻¹' s)- Defined in
- Mathlib.Topology.Constructible
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- nhdsproof · cited by 5,554
- Set.preimagestatement and proof · cited by 4,946
- IsOpenproof · cited by 2,400
- Continuous.continuousAtproof · cited by 297
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- IsOpen.preimageproof · cited by 147
- ContinuousAt.preimage_mem_nhdsproof · cited by 46
- Topology.IsConstructibleproof · cited by 45
- Topology.IsOpenEmbedding.continuousproof · cited by 23
- Topology.IsLocallyConstructiblestatement and proof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- Topology.IsLocallyConstructible.of_isOpenCover'proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isLocallyConstructible_imageproof · cited by 1
- Topology.IsLocallyConstructible.iff_of_isOpenCoverproof · cited by 0