Theorems · Theorem · general topology
IsCountablyCompact.union
∀ {E : Type u_2} [inst : TopologicalSpace E] {A B : Set E},
IsCountablyCompact A → IsCountablyCompact B → IsCountablyCompact (A ∪ B)The union of two countably compact sets is countably compact.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 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.
Cites14
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
- LE.le.transproof · cited by 3,151
- Set.iUnionproof · cited by 2,483
- IsOpenproof · cited by 2,400
- Set.extproof · cited by 2,266
- Set.Finiteproof · cited by 1,814
- Set.iUnion_congr_Propproof · cited by 374
- Set.subset_union_leftproof · cited by 142
- Set.subset_union_rightproof · cited by 123
- Set.Finite.unionproof · cited by 74
- IsCountablyCompactstatement and proof · cited by 33
Cited by1
Results whose statement or proof uses this declaration.
- Finset.isCountablyCompact_biUnionproof · cited by 1