Theorems · Theorem · general topology
Perfect.subset_perfectKernel
∀ {X : Type u} [inst : TopologicalSpace X] {s P : Set X}, Perfect P → P ⊆ s → P ⊆ CantorBendixson.perfectKernel sEvery perfect subset of a set is contained in its perfect kernel.
- Defined in
- Mathlib.Topology.CantorBendixson
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 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.
Cites10
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
- Ordinalproof · cited by 1,688
- Perfectstatement and proof · cited by 17
- Set.subset_iInterproof · cited by 17
- CantorBendixson.iteratedDerivedSetproof · cited by 13
- CantorBendixson.perfectKernelstatement · cited by 9
- Perfect.accproof · cited by 6
- CantorBendixson.iteratedDerivedSet_monoproof · cited by 2
- CantorBendixson.iteratedDerivedSet_constant_iff_preperfectproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CantorBendixson.perfectKernel_idemproof · cited by 0