Theorems · Theorem · general topology
closure_sUnion
∀ {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] (S : Set (Set α)),
closure (⋃₀ S) = ⋃ s ∈ S, closure s- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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 and proof · cited by 2,483
- closurestatement and proof · cited by 1,254
- Set.sUnionstatement · cited by 392
- Set.sUnion_eq_biUnionproof · cited by 51
- AlexandrovDiscretestatement and proof · cited by 45
- closure_iUnionproof · cited by 1
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