Theorems · Theorem · general topology
isClosed_iff_derivedSet_subset
∀ {X : Type u_1} [inst : TopologicalSpace X] (A : Set X), IsClosed A ↔ derivedSet A ⊆ A- Defined in
- Mathlib.Topology.DerivedSet
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 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.
Cites12
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
- LE.le.transproof · cited by 3,151
- IsClosedstatement and proof · cited by 1,639
- Filter.principalproof · cited by 740
- ClusterPtproof · cited by 138
- Set.sdiff_singleton_eq_selfproof · cited by 38
- derivedSetstatement and proof · cited by 16
- IsClosed.closure_subsetproof · cited by 11
- isClosed_iff_clusterPtproof · cited by 7
- accPt_principal_iff_clusterPtproof · cited by 4
- derivedSet_subset_closureproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IsClosed.relDerivedSet_eqproof · cited by 2
- perfect_iff_eq_derivedSetproof · cited by 1
- isClosed_derivedSetproof · cited by 0