Theorems · Theorem · general topology
IsClosed.relDerivedSet_eq
∀ {X : Type u_1} [inst : TopologicalSpace X] {A : Set X}, IsClosed A → relDerivedSet A = derivedSet A- Defined in
- Mathlib.Topology.DerivedSet
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsClosedstatement and proof · cited by 1,639
- OrderHomstatement · cited by 934
- derivedSetstatement · cited by 16
- relDerivedSetstatement · cited by 14
- isClosed_iff_derivedSet_subsetproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- CantorBendixson.isClosed_iteratedDerivedSetproof · cited by 2
- CantorBendixson.perfect_perfectKernelproof · cited by 1