Theorems · Theorem · general topology
Ultrafilter.le_nhds_lim
∀ {X : Type u} [inst : TopologicalSpace X] [CompactSpace X] (F : Ultrafilter X), ↑F ≤ nhds F.lim- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCompactSpace
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Set.univproof · cited by 3,945
- CompactSpacestatement and proof · cited by 593
- Ultrafilterstatement and proof · cited by 193
- Ultrafilter.toFilterstatement and proof · cited by 172
- isCompact_univproof · cited by 53
- Filter.principal_univproof · cited by 46
- IsCompact.ultrafilter_le_nhdsproof · cited by 5
- le_nhds_limproof · cited by 5
- Ultrafilter.limstatement and proof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Ultrafilter.lim_eq_iff_le_nhdsproof · cited by 2
- isOpen_iff_ultrafilter'proof · cited by 0