Theorems · Theorem · general topology
ClusterPt.mono
∀ {X : Type u} [inst : TopologicalSpace X] {x : X} {f g : Filter X}, ClusterPt x f → f ≤ g → ClusterPt x g- Defined in
- Mathlib.Topology.ClusterPt
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
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
- nhdsproof · cited by 5,554
- ClusterPtstatement and proof · cited by 138
- inf_le_inf_leftproof · cited by 25
- Filter.NeBot.monoproof · cited by 17
Cited by30
Results whose statement or proof uses this declaration.
- IsCompact.isClosedproof · cited by 77
- IsCompact.inter_rightproof · cited by 30
- MapClusterPt.monoproof · cited by 6
- AccPt.clusterPtproof · cited by 6
- isProperMap_iff_isClosedMap_and_compact_fibersproof · cited by 5
- IsLindelof.inter_rightproof · cited by 4
- MapClusterPt.of_compproof · cited by 4
- tangentConeAt_monoproof · cited by 4
- tangentConeAt_mono_fieldproof · cited by 3
- mem_tangentConeAt_of_frequentlyproof · cited by 3
- isCompact_iff_ultrafilter_le_nhdsproof · cited by 3
- isCountablyCompact_iff_seq_clusterPtproof · cited by 2