Theorems · Theorem · general topology
quasiSeparatedSpace_iff
∀ (α : Type u_3) [inst : TopologicalSpace α], QuasiSeparatedSpace α ↔ ∀ (U V : Set α), IsOpen U → IsCompact U → IsOpen V → IsCompact V → IsCompact (U ∩ V)
- Defined in
- Mathlib.Topology.QuasiSeparated
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, 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
- IsOpenstatement and proof · cited by 2,400
- IsCompactstatement and proof · cited by 1,282
- QuasiSeparatedSpacestatement and proof · cited by 49
- QuasiSeparatedSpace.casesOnproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- isQuasiSeparated_univ_iffproof · cited by 4
- AlgebraicGeometry.quasiSeparatedSpace_iff_forall_affineOpensproof · cited by 1