Theorems · Inductive type · general topology
AlexandrovDiscrete
(α : Type u_1) → [TopologicalSpace α] → Prop
A topological space is Alexandrov-discrete or finitely generated if the intersection of a family of open sets is open.
- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 45 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 by54
Results whose statement or proof uses this declaration.
- AlexDisc.ofstatement and proof · cited by 5
- isOpen_sInterstatement and proof · cited by 5
- principal_nhdsKerstatement and proof · cited by 4
- principal_nhdsKer_singletonstatement and proof · cited by 4
- isOpen_nhdsKerstatement and proof · cited by 4
- isOpen_iInterstatement and proof · cited by 3
- interior_iInterstatement and proof · cited by 2
- isClosed_iUnionstatement and proof · cited by 2
- isClosed_sUnionstatement and proof · cited by 2
- isOpen_iInter₂statement and proof · cited by 2
- AlexDisc.mk.injstatement and proof · cited by 1
- AlexDisc.mk.noConfusionstatement and proof · cited by 1