Theorems · Theorem · general topology
AccPt.mono
∀ {X : Type u} [inst : TopologicalSpace X] {x : X} {F G : Filter X}, AccPt x F → F ≤ G → AccPt x GIf x is an accumulation point of F and F ≤ G, then
x is an accumulation point of G.
- Defined in
- Mathlib.Topology.ClusterPt
- Cited by
- 7 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.
Cites7
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
- Compl.complproof · cited by 2,925
- nhdsWithinproof · cited by 1,912
- AccPtstatement and proof · cited by 75
- inf_le_inf_leftproof · cited by 25
- Filter.NeBot.monoproof · cited by 17
Cited by7
Results whose statement or proof uses this declaration.
- derivedSet_monoproof · cited by 3
- Preperfect.perfect_closureproof · cited by 3
- Set.Infinite.exists_accPt_of_subset_isCompactproof · cited by 2
- Set.Infinite.exists_accPt_principalproof · cited by 1
- Ordinal.IsClosedBelow.sInterproof · cited by 1
- continuousAt_of_not_accPt_topproof · cited by 0
- Ordinal.IsAcc.monoproof · cited by 0