Theorems · Theorem · general topology
isOpen_iInter
∀ {ι : Sort u_1} {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] {f : ι → Set α},
(∀ (i : ι), IsOpen (f i)) → IsOpen (⋂ i, f i)- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, 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
- IsOpenstatement and proof · cited by 2,400
- Set.iInterstatement · cited by 1,084
- Set.forall_mem_rangeproof · cited by 135
- AlexandrovDiscretestatement and proof · cited by 45
- isOpen_sInterproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- interior_iInterproof · cited by 2
- isOpen_iInter₂proof · cited by 2
- isClopen_iInterproof · cited by 1