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Theorems · Theorem · general topology

Set.isCompact_sigma

∀ {ι : Type u_1} {X : ι → Type u_2} [inst : (i : ι) → TopologicalSpace (X i)] {s : Set ι} {t : (i : ι) → Set (X i)},
  s.Finite → (∀ i ∈ s, IsCompact (t i)) → IsCompact (s.sigma t)
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
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsCompactOpenCovered.iff_isCompactOpenCovered_sigmaMk · cited by 3IsCompactOpenCovered.iff_…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Finite · cited by 1814Set.FiniteIsCompact · cited by 1282IsCompactIsCompact.image · cited by 105IsCompact.imageSet.sigma · cited by 65Set.sigmaSet.Finite.isCompact_biUnion · cited by 11Finite.isCompact_biUnioncontinuous_sigmaMk · cited by 8continuous_sigmaMkSet.sigma_eq_biUnion · cited by 1Set.sigma_eq_biUnionSet.isCompact_sigmaCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.