Theorems · Definition · general topology
derivedSet
{X : Type u_1} → [TopologicalSpace X] → Set X → Set XThe derived set of a set is the set of all accumulation points of it.
- Defined in
- Mathlib.Topology.DerivedSet
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredproof · cited by 6,101
- Filter.principalproof · cited by 740
- AccPtproof · cited by 75
Cited by17
Results whose statement or proof uses this declaration.
- relDerivedSetproof · cited by 14
- derivedSet_monostatement and proof · cited by 3
- isClosed_iff_derivedSet_subsetstatement and proof · cited by 3
- IsClosed.relDerivedSet_eqstatement · cited by 2
- CantorBendixson.isClosed_iteratedDerivedSetproof · cited by 2
- derivedSet_closurestatement and proof · cited by 1
- derivedSet_subset_closurestatement and proof · cited by 1
- derivedSet_unionstatement · cited by 1
- preperfect_iff_eq_relDerivedSetproof · cited by 1
- preperfect_iff_subset_derivedSetstatement · cited by 1
- perfect_iff_eq_derivedSetstatement and proof · cited by 1
- mem_derivedSetstatement · cited by 1