Theorems · Definition · algebraic geometry
Topology.IsLocallyConstructible
{X : Type u_2} → [TopologicalSpace X] → Set X → PropA set in a topological space is locally constructible, if every point has a neighborhood on which the set is constructible.
- Defined in
- Mathlib.Topology.Constructible
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.preimageproof · cited by 4,946
- IsOpenproof · cited by 2,400
- Topology.IsConstructibleproof · cited by 45
Cited by22
Results whose statement or proof uses this declaration.
- Topology.IsConstructible.isLocallyConstructiblestatement · cited by 7
- Topology.IsLocallyConstructible.of_isOpenCoverstatement and proof · cited by 3
- Topology.IsLocallyConstructible.preimage_of_isOpenEmbeddingstatement and proof · cited by 3
- Topology.IsLocallyConstructible.unionstatement and proof · cited by 3
- Topology.IsLocallyConstructible.emptystatement · cited by 3
- Topology.IsLocallyConstructible.interstatement and proof · cited by 2
- Topology.IsLocallyConstructible.isConstructiblestatement and proof · cited by 2
- Topology.IsLocallyConstructible.isConstructible_of_subset_of_isCompactstatement and proof · cited by 2
- Topology.IsLocallyConstructible.univstatement · cited by 2
- Topology.IsLocallyConstructible.finsetInfstatement and proof · cited by 1
- Topology.IsLocallyConstructible.iUnionstatement and proof · cited by 1
- Topology.IsLocallyConstructible.inter_of_isOpen_isCompactstatement and proof · cited by 1