Theorems · Theorem · general topology
isClosed_iUnion
∀ {ι : Sort u_1} {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] {f : ι → Set α},
(∀ (i : ι), IsClosed (f i)) → IsClosed (⋃ i, f i)- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 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.iUnionstatement · cited by 2,483
- IsClosedstatement and proof · cited by 1,639
- Set.forall_mem_rangeproof · cited by 135
- AlexandrovDiscretestatement and proof · cited by 45
- isClosed_sUnionproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- isClopen_iUnionproof · cited by 1
- isClosed_iUnion₂proof · cited by 0