Theorems · Theorem · general topology
isCompact_accumulate
∀ {X : Type u} [inst : TopologicalSpace X] {K : ℕ → Set X},
(∀ (n : ℕ), IsCompact (K n)) → ∀ (n : ℕ), IsCompact (Set.accumulate K n)- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.ofPredproof · cited by 6,101
- IsCompactstatement and proof · cited by 1,282
- Set.accumulatestatement · cited by 32
- Set.finite_le_natproof · cited by 16
- Set.Finite.isCompact_biUnionproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- isCompact_compactCoveringproof · cited by 8
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2