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Theorems · Theorem · general topology

isSigmaCompact_sUnion

∀ {X : Type u_1} [inst : TopologicalSpace X] (S : Set (Set X)),
  S.Countable → (∀ (s : ↑S), IsSigmaCompact ↑s) → IsSigmaCompact (⋃₀ S)

Countable unions of σ-compact sets are σ-compact.

Defined in
Mathlib.Topology.Compactness.SigmaCompact
Cited by
0 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemCountable · cited by 633CountableSet.Countable · cited by 545Set.CountableSet.sUnion · cited by 392Set.sUnionSet.sUnion_eq_iUnion · cited by 26Set.sUnion_eq_iUnionIsSigmaCompact · cited by 24IsSigmaCompactSet.countable_coe_iff · cited by 15Set.countable_coe_iffisSigmaCompact_iUnion · cited by 2isSigmaCompact_iUnionisSigmaCompact_sUnionCITED BYCITES

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