Theorems · Theorem · algebraic geometry
Topology.IsConstructible.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.IsOpenEmbedding f → Topology.IsConstructible s → Topology.IsConstructible (f ⁻¹' s)[Stacks Tag 005J](https://stacks.math.columbia.edu/tag/005J)
- Defined in
- Mathlib.Topology.Constructible
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.preimagestatement · cited by 4,946
- IsOpenproof · cited by 2,400
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsConstructiblestatement and proof · cited by 45
- IsRetrocompactproof · cited by 43
- Topology.IsOpenEmbedding.continuousproof · cited by 23
- Topology.IsConstructible.preimageproof · cited by 3
- IsRetrocompact.preimage_of_isOpenEmbeddingproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Topology.IsLocallyConstructible.of_isOpenCoverproof · cited by 3
- Topology.IsLocallyConstructible.preimage_of_isOpenEmbeddingproof · cited by 3
- Topology.IsLocallyConstructible.unionproof · cited by 3
- Topology.IsLocallyConstructible.isConstructible_of_subset_of_isCompactproof · cited by 2
- Topology.IsLocallyConstructible.interproof · cited by 2
- Topology.isConstructible_preimage_iff_of_isOpenEmbeddingproof · cited by 1