Theorems · Theorem · general topology
CantorBendixson.isClosed_iteratedDerivedSet
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X},
IsClosed s → ∀ (a : Ordinal.{u}), IsClosed (CantorBendixson.iteratedDerivedSet s a)- Defined in
- Mathlib.Topology.CantorBendixson
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 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.
Cites18
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.Elemproof · cited by 7,166
- Ordinalstatement and proof · cited by 1,688
- IsClosedstatement and proof · cited by 1,639
- Set.Iioproof · cited by 1,166
- Set.iInterproof · cited by 1,084
- Order.IsSuccLimitproof · cited by 255
- Set.iInter_congr_Propproof · cited by 170
- isClosed_iInterproof · cited by 43
- Ordinal.limitRecOnproof · cited by 20
- Set.iInter_coe_setproof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- CantorBendixson.perfect_perfectKernelproof · cited by 1
- CantorBendixson.isClosed_perfectKernelproof · cited by 0