Theorems · Theorem · general topology
Ultrafilter.clusterPt_iff
∀ {X : Type u} {x : X} [inst : TopologicalSpace X] {f : Ultrafilter X}, ClusterPt x ↑f ↔ ↑f ≤ nhds x- Defined in
- Mathlib.Topology.Ultrafilter
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
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Cites8
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
- Ultrafilterstatement and proof · cited by 193
- Ultrafilter.toFilterstatement and proof · cited by 172
- ClusterPtstatement · cited by 138
- ClusterPt.of_le_nhdsproof · cited by 7
- Ultrafilter.le_of_inf_neBot'proof · cited by 1
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