Theorems · Theorem · general topology
preperfect_iff_perfect_closure
∀ {α : Type u_1} [inst : TopologicalSpace α] {C : Set α} [T1Space α], Preperfect C ↔ Perfect (closure C)In a T1 space, being preperfect is equivalent to having perfect closure.
- Defined in
- Mathlib.Topology.Perfect
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
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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
- nhdsproof · cited by 5,554
- closurestatement and proof · cited by 1,254
- Filter.principalproof · cited by 740
- Filter.Frequentlyproof · cited by 414
- subset_closureproof · cited by 309
- T1Spacestatement and proof · cited by 275
- AccPtproof · cited by 75
- Filter.Frequently.monoproof · cited by 64
- Preperfectstatement and proof · cited by 19
- Perfectstatement and proof · cited by 17
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