Theorems · Theorem · general topology
ClusterPt.of_le_nhds
∀ {X : Type u} [inst : TopologicalSpace X] {x : X} {f : Filter X}, f ≤ nhds x → ∀ [f.NeBot], ClusterPt x f- Defined in
- Mathlib.Topology.ClusterPt
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpaceFilter.NeBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.NeBotstatement and proof · cited by 853
- ClusterPtstatement · cited by 138
- inf_eq_rightproof · cited by 64
Cited by7
Results whose statement or proof uses this declaration.
- Filter.Tendsto.mapClusterPtproof · cited by 4
- ClusterPt.of_le_nhds'proof · cited by 3
- IsCompact.le_nhdsSet_of_clusterPtproof · cited by 2
- isComplete_iff_ultrafilterproof · cited by 1
- Filter.Tendsto.inseparable_iff_uniformityproof · cited by 1
- Ultrafilter.clusterPt_iffproof · cited by 0
- isCountablyCompact_singletonproof · cited by 0