Theorems · Theorem · general topology
isQuasiSeparated_iff_quasiSeparatedSpace
∀ {α : Type u_1} [inst : TopologicalSpace α] (s : Set α), IsOpen s → (IsQuasiSeparated s ↔ QuasiSeparatedSpace ↑s)- Defined in
- Mathlib.Topology.QuasiSeparated
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 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.
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
- Set.Elemstatement · cited by 7,166
- Set.imageproof · cited by 5,609
- Set.univproof · cited by 3,945
- IsOpenstatement and proof · cited by 2,400
- Set.image_univproof · cited by 322
- Subtype.range_coe_subtypeproof · cited by 170
- QuasiSeparatedSpacestatement · cited by 49
- IsOpen.isOpenEmbedding_subtypeValproof · cited by 32
- IsQuasiSeparatedstatement and proof · cited by 17
- isQuasiSeparated_univ_iffproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.isQuasiSeparatedproof · cited by 2
- AlgebraicGeometry.exists_isAffineOpen_preimage_eqproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isQuasiSeparated_preimageproof · cited by 1