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Theorems · Theorem · general topology

isClosed_sUnion

∀ {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] {S : Set (Set α)},
  (∀ s ∈ S, IsClosed s) → IsClosed (⋃₀ S)
Defined in
Mathlib.Topology.AlexandrovDiscrete
Cited by
2 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceAlexandrovDiscrete
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isClosed_iUnion · cited by 2isClosed_iUnionisClopen_sUnion · cited by 0isClopen_sUnionSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsClosed · cited by 1639IsClosedSet.sUnion · cited by 392Set.sUnionAlexandrovDiscrete · cited by 45AlexandrovDiscretealexandrovDiscrete_iff_isClosed · cited by 1alexandrovDiscrete_iff_is…isClosed_sUnionCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.