Theorems · Theorem · general topology
Perfect.closure_nhds_inter
∀ {α : Type u_1} [inst : TopologicalSpace α] {C U : Set α},
Perfect C → ∀ x ∈ C, x ∈ U → IsOpen U → Perfect (closure (U ∩ C)) ∧ (closure (U ∩ C)).Nonempty- Defined in
- Mathlib.Topology.Perfect
- Cited by
- 1 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.
Cites10
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
- Set.Nonemptystatement · cited by 2,627
- IsOpenstatement and proof · cited by 2,400
- closurestatement · cited by 1,254
- Perfectstatement and proof · cited by 17
- Set.Nonempty.closureproof · cited by 6
- Perfect.accproof · cited by 6
- Preperfect.perfect_closureproof · cited by 3
- Preperfect.open_interproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Perfect.splittingproof · cited by 1