Theorems · Inductive type · general topology
QuasiSeparatedSpace
(α : Type u_3) → [TopologicalSpace α] → Prop
A topological space is quasi-separated if the intersections of any pairs of compact open subsets are still compact.
- Defined in
- Mathlib.Topology.QuasiSeparated
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by53
Results whose statement or proof uses this declaration.
- isQuasiSeparated_univstatement and proof · cited by 6
- IsCompact.isRetrocompactstatement and proof · cited by 4
- isQuasiSeparated_univ_iffstatement · cited by 4
- IsCompact.inter_of_isOpenstatement and proof · cited by 3
- AlgebraicGeometry.quasiSeparatedSpace_of_quasiSeparatedstatement and proof · cited by 3
- isQuasiSeparated_iff_quasiSeparatedSpacestatement · cited by 3
- AlgebraicGeometry.quasiCompact_iff_compactSpacestatement and proof · cited by 2
- IsCompact.isConstructiblestatement and proof · cited by 2
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.IsQuasiAffine.of_forall_exists_mem_basicOpenproof · cited by 2
- Topology.IsLocallyConstructible.isConstructiblestatement and proof · cited by 2
- Topology.IsLocallyConstructible.isConstructible_of_subset_of_isCompactstatement and proof · cited by 2