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Theorems · Theorem · general topology

Set.Finite.isCompact_sUnion

∀ {X : Type u} [inst : TopologicalSpace X] {S : Set (Set X)}, S.Finite → (∀ s ∈ S, IsCompact s) → IsCompact (⋃₀ S)
Defined in
Mathlib.Topology.Compactness.Compact
Cited by
1 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

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isCompact_iUnion · cited by 6isCompact_iUnionSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Finite · cited by 1814Set.FiniteIsCompact · cited by 1282IsCompactSet.sUnion · cited by 392Set.sUnionSet.sUnion_eq_biUnion · cited by 51Set.sUnion_eq_biUnionSet.Finite.isCompact_biUnion · cited by 11Finite.isCompact_biUnionFinite.isCompact_sUnionCITED BYCITES

Cites7

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Cited by1

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