Theorems · Theorem · general topology
IsOpen.perfect_closure
∀ {α : Type u_1} [inst : TopologicalSpace α] [PerfectSpace α] {U : Set α}, IsOpen U → Perfect (closure U)- Defined in
- Mathlib.Topology.Perfect
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpacePerfectSpace
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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenstatement and proof · cited by 2,400
- closurestatement · cited by 1,254
- Perfectstatement · cited by 17
- PerfectSpacestatement and proof · cited by 7
- Preperfect.perfect_closureproof · cited by 3
- IsOpen.preperfectproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAtproof · cited by 1
- Complex.CanonicalDecomp.divisor_eq_divisorproof · cited by 1