Theorems · Theorem · general topology
IsLindelof.compl_mem_sets
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X},
IsLindelof s → ∀ {f : Filter X} [CountableInterFilter f], (∀ x ∈ s, sᶜ ∈ nhds x ⊓ f) → sᶜ ∈ fThe complement to a Lindelöf set belongs to a filter f with the countable intersection
property if it belongs to each filter 𝓝 x ⊓ f, x ∈ s.
- Defined in
- Mathlib.Topology.Compactness.Lindelof
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Compl.complstatement and proof · cited by 2,925
- Filter.NeBotproof · cited by 853
- Filter.principalproof · cited by 740
- inf_le_rightproof · cited by 238
- compl_complproof · cited by 229
- IsLindelofstatement and proof · cited by 85
- CountableInterFilterstatement and proof · cited by 78
- inf_assocproof · cited by 53
Cited by1
Results whose statement or proof uses this declaration.
- IsLindelof.compl_mem_sets_of_nhdsWithinproof · cited by 2