Theorems · Theorem · general topology
isLindelof_singleton
∀ {X : Type u} [inst : TopologicalSpace X] {x : X}, IsLindelof {x}A singleton set is a Lindelof set.
- Defined in
- Mathlib.Topology.Compactness.Lindelof
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterproof · cited by 8,121
- nhdsproof · cited by 5,554
- LE.le.transproof · cited by 3,151
- Filter.NeBotproof · cited by 853
- Filter.principalproof · cited by 740
- IsLindelofstatement · cited by 85
- CountableInterFilterproof · cited by 78
- pure_le_nhdsproof · cited by 39
- Filter.principal_singletonproof · cited by 31
- ClusterPt.of_le_nhds'proof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Set.Finite.isLindelofproof · cited by 1
- Set.Countable.isLindelofproof · cited by 1
- IsLindelof.insertproof · cited by 0
- Set.Subsingleton.isLindelofproof · cited by 0