Theorems · Theorem · general topology
closure_iUnion
∀ {ι : Sort u_1} {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] (f : ι → Set α),
closure (⋃ i, f i) = ⋃ i, closure (f i)- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 1 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.
Cites11
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
- Compl.complproof · cited by 2,925
- Set.iUnionstatement and proof · cited by 2,483
- closurestatement and proof · cited by 1,254
- Set.iInterproof · cited by 1,084
- interiorproof · cited by 714
- AlexandrovDiscretestatement and proof · cited by 45
- Set.compl_iUnionproof · cited by 32
- compl_injectiveproof · cited by 22
- interior_iInterproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- closure_sUnionproof · cited by 0