Theorems · Theorem · general topology
IsLindelof.countable_of_discrete
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X} [DiscreteTopology X], IsLindelof s → s.Countable- Defined in
- Mathlib.Topology.Compactness.Lindelof
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- nhdsproof · cited by 5,554
- Set.iUnionproof · cited by 2,483
- Set.Countablestatement and proof · cited by 545
- DiscreteTopologystatement and proof · cited by 373
- IsLindelofstatement and proof · cited by 85
- Set.biUnion_of_singletonproof · cited by 43
- Set.Countable.monoproof · cited by 34
- nhds_discreteproof · cited by 23
- IsLindelof.elim_nhds_subcoverproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- countable_of_Lindelof_of_discreteproof · cited by 1
- isLindelof_iff_countableproof · cited by 0