Theorems · Definition · general topology
Ultrafilter.lim
{X : Type u_1} → [TopologicalSpace X] → Ultrafilter X → XIf F is an ultrafilter, then Filter.Ultrafilter.lim F is a limit of the filter, if it exists.
Note that dot notation F.lim can be used for F : Filter.Ultrafilter X.
- Defined in
- Mathlib.Topology.Defs.Ultrafilter
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 55 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Ultrafilterstatement and proof · cited by 193
- Ultrafilter.toFilterproof · cited by 172
- Filter.limproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- Ultrafilter.le_nhds_limstatement and proof · cited by 2
- Ultrafilter.lim_eq_iff_le_nhdsstatement and proof · cited by 2
- isOpen_iff_ultrafilter'statement and proof · cited by 0
- Compactum.lim_eq_strstatement · cited by 0
- Compactum.ofTopologicalSpaceproof · cited by 0