Theorems · Theorem · general topology
Preperfect.perfect_closure
∀ {α : Type u_1} [inst : TopologicalSpace α] {C : Set α}, Preperfect C → Perfect (closure C)The closure of a preperfect set is perfect.
For a converse, see preperfect_iff_perfect_closure.
- Defined in
- Mathlib.Topology.Perfect
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 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.
Cites17
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
- Filterproof · cited by 8,121
- nhdsproof · cited by 5,554
- Compl.complproof · cited by 2,925
- closurestatement and proof · cited by 1,254
- Filter.NeBotproof · cited by 853
- Filter.principalproof · cited by 740
- subset_closureproof · cited by 309
- isClosed_closureproof · cited by 195
- inf_assocproof · cited by 53
- Filter.principal_monoproof · cited by 30
Cited by3
Results whose statement or proof uses this declaration.
- IsOpen.perfect_closureproof · cited by 2
- Perfect.closure_nhds_interproof · cited by 1
- preperfect_iff_perfect_closureproof · cited by 0