Theorems · Theorem · general topology
isLindelof_iUnion
∀ {X : Type u} [inst : TopologicalSpace X] {ι : Sort u_2} {f : ι → Set X} [Countable ι],
(∀ (i : ι), IsLindelof (f i)) → IsLindelof (⋃ i, f i)- Defined in
- Mathlib.Topology.Compactness.Lindelof
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCountable
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.iUnionstatement · cited by 2,483
- Countablestatement and proof · cited by 633
- Set.forall_mem_rangeproof · cited by 135
- IsLindelofstatement and proof · cited by 85
- Set.countable_rangeproof · cited by 31
- Set.Countable.isLindelof_sUnionproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsLindelof.unionproof · cited by 3
- IsSigmaCompact.isLindelofproof · cited by 0