Theorems · Theorem · general topology
isClopen_sUnion
∀ {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] {S : Set (Set α)},
(∀ s ∈ S, IsClopen s) → IsClopen (⋃₀ S)- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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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.sUnionstatement · cited by 392
- IsClopenstatement and proof · cited by 189
- AlexandrovDiscretestatement and proof · cited by 45
- isOpen_sUnionproof · cited by 15
- isClosed_sUnionproof · cited by 2
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