Theorems · Theorem · general topology
IsCompact.sigma_exists_finite_sigma_eq
∀ {ι : Type u_1} {X : ι → Type u_2} [inst : (i : ι) → TopologicalSpace (X i)] (u : Set ((i : ι) × X i)),
IsCompact u → ∃ s t, s.Finite ∧ (∀ (i : ι), IsCompact (t i)) ∧ s.sigma t = u- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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.
Cites24
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.univproof · cited by 3,945
- Set.iUnionproof · cited by 2,483
- Set.extproof · cited by 2,266
- Set.Finitestatement · cited by 1,814
- IsCompactstatement and proof · cited by 1,282
- Set.image_univproof · cited by 322
Cited by1
Results whose statement or proof uses this declaration.
- IsCompactOpenCovered.iff_isCompactOpenCovered_sigmaMkproof · cited by 3