Theorems · Theorem · general topology
isClopen_iInter
∀ {ι : Sort u_1} {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] {f : ι → Set α},
(∀ (i : ι), IsClopen (f i)) → IsClopen (⋂ i, f i)- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.iInterstatement · cited by 1,084
- IsClopenstatement and proof · cited by 189
- AlexandrovDiscretestatement and proof · cited by 45
- isClosed_iInterproof · cited by 43
- isOpen_iInterproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- isClopen_iInter₂proof · cited by 0