Theorems · Theorem · algebraic geometry
Topology.IsLocallyConstructible.inter_of_isOpen_isCompact
∀ {X : Type u_2} [inst : TopologicalSpace X] {s t : Set X} [PrespectralSpace X] [QuasiSeparatedSpace X],
Topology.IsLocallyConstructible s → IsOpen t → IsCompact t → Topology.IsConstructible (s ∩ t)- Defined in
- Mathlib.Topology.Constructible
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 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
- IsOpenstatement and proof · cited by 2,400
- IsCompactstatement and proof · cited by 1,282
- Set.inter_subset_rightproof · cited by 329
- QuasiSeparatedSpacestatement and proof · cited by 49
- Topology.IsConstructiblestatement · cited by 45
- PrespectralSpacestatement and proof · cited by 23
- Topology.IsLocallyConstructiblestatement and proof · cited by 22
- Topology.IsConstructible.isLocallyConstructibleproof · cited by 7
- Topology.IsLocallyConstructible.interproof · cited by 2
- Topology.IsLocallyConstructible.isConstructible_of_subset_of_isCompactproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsLocallyConstructible.iff_isConstructible_of_isOpenCoverproof · cited by 0