Theorems · Theorem · general topology
Set.Countable.isLindelof_biUnion
∀ {X : Type u} {ι : Type u_1} [inst : TopologicalSpace X] {s : Set ι} {f : ι → Set X},
s.Countable → (∀ i ∈ s, IsLindelof (f i)) → IsLindelof (⋃ i ∈ s, f i)- Defined in
- Mathlib.Topology.Compactness.Lindelof
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 87 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.
Cites18
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 and proof · cited by 2,483
- IsOpenproof · cited by 2,400
- Set.Countablestatement and proof · cited by 545
- Set.iUnion_congr_Propproof · cited by 374
- Function.sometimesproof · cited by 86
- IsLindelofstatement and proof · cited by 85
- Function.sometimes_specproof · cited by 84
- subset_transproof · cited by 63
- Set.iUnion₂_subsetproof · cited by 48
- Set.iUnion_existsproof · cited by 45
Cited by4
Results whose statement or proof uses this declaration.
- Set.Finite.isLindelof_biUnionproof · cited by 4
- Set.Countable.isLindelofproof · cited by 1
- Set.Countable.isLindelof_sUnionproof · cited by 1
- isLindelof_open_iff_eq_countable_iUnion_of_isTopologicalBasisproof · cited by 0