Theorems · Inductive type · general topology
QuasiSober
(α : Type u_3) → [TopologicalSpace α] → Prop
A space is sober if every irreducible closed subset has a generic point.
- Defined in
- Mathlib.Topology.Sober
- Cited by
- 31 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 by40
Results whose statement or proof uses this declaration.
- genericPointstatement and proof · cited by 15
- IsIrreducible.genericPointstatement and proof · cited by 8
- genericPoint_specstatement and proof · cited by 7
- genericPoints.ofComponentstatement and proof · cited by 6
- IsIrreducible.isGenericPoint_genericPoint_closurestatement and proof · cited by 6
- irreducibleSetEquivPointsstatement and proof · cited by 3
- QuasiSober.soberstatement and proof · cited by 3
- genericPoints.component_ofComponentstatement and proof · cited by 2
- genericPoints.equivstatement and proof · cited by 2
- genericPoints.isGenericPoint_ofComponentstatement and proof · cited by 2
- IsIrreducible.isGenericPoint_genericPointstatement and proof · cited by 2
- Topology.IsOpenEmbedding.quasiSoberstatement and proof · cited by 2