Theorems · Definition · general topology
Ultrafilter.of
{α : Type u} → (f : Filter α) → [f.NeBot] → Ultrafilter αConstruct an ultrafilter extending a given filter. The ultrafilter lemma is the assertion that such a filter exists; we use the axiom of choice to pick one.
- Defined in
- Mathlib.Order.Filter.Ultrafilter.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.NeBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Filter.NeBotstatement and proof · cited by 853
- Ultrafilterstatement · cited by 193
- Ultrafilter.exists_leproof · cited by 2
Cited by17
Results whose statement or proof uses this declaration.
- Filter.hyperfilterproof · cited by 30
- Ultrafilter.of_lestatement · cited by 15
- FirstOrder.Language.Theory.isSatisfiable_iff_isFinitelySatisfiableproof · cited by 3
- Ultrafilter.ofComapInfPrincipalproof · cited by 2
- Filter.totallyBounded_iff_filterproof · cited by 2
- Cauchy.ultrafilter_ofstatement and proof · cited by 1
- Ultrafilter.exists_ultrafilter_of_finite_inter_nonemptyproof · cited by 1
- Filter.forall_neBot_le_iffproof · cited by 1
- isComplete_iff_ultrafilterproof · cited by 1
- IsFoelner.amenableproof · cited by 1
- IsAddFoelner.amenableproof · cited by 1
- Filter.totallyBounded_iff_ultrafilterproof · cited by 1