Theorems · Definition · general topology
relDerivedSet
{X : Type u_1} → [TopologicalSpace X] → Set X →o Set XThe relative derived set operator viewed as a monotone self-map of Set X.
- Defined in
- Mathlib.Topology.DerivedSet
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- OrderHomstatement · cited by 934
- derivedSetproof · cited by 16
Cited by15
Results whose statement or proof uses this declaration.
- CantorBendixson.iteratedDerivedSetproof · cited by 13
- relDerivedSet_subsetstatement · cited by 3
- CantorBendixson.iteratedDerivedSet_succstatement and proof · cited by 2
- CantorBendixson.iteratedDerivedSet_zeroproof · cited by 2
- IsClosed.relDerivedSet_eqstatement · cited by 2
- CantorBendixson.iteratedDerivedSet_monoproof · cited by 2
- CantorBendixson.perfectKernel_eq_iteratedDerivedSet_of_mem_fixedPointsstatement and proof · cited by 1
- CantorBendixson.perfect_perfectKernelproof · cited by 1
- preperfect_iff_eq_relDerivedSetstatement · cited by 1
- CantorBendixson.iteratedDerivedSet_antitoneproof · cited by 1
- CantorBendixson.iteratedDerivedSet_constant_iff_preperfectproof · cited by 1
- CantorBendixson.iteratedDerivedSet_limitproof · cited by 1