Theorems · Theorem · general topology
IsLindelof.countable
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, IsLindelof s → DiscreteTopology ↑s → s.Countable- Defined in
- Mathlib.Topology.Compactness.Lindelof
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 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.
Cites8
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 and proof · cited by 7,166
- Set.Countablestatement · cited by 545
- DiscreteTopologystatement and proof · cited by 373
- IsLindelofstatement and proof · cited by 85
- Set.countable_coe_iffproof · cited by 15
- countable_of_Lindelof_of_discreteproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsLindelof.countable_of_isDiscreteproof · cited by 1