Theorems · Definition · general topology
IsCompactSystem
{α : Type u_1} → Set (Set α) → PropA set of sets is a compact system if, whenever a countable subfamily has empty intersection, then finitely many of them already have empty intersection.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Set.iInterproof · cited by 1,084
- Set.dissipateproof · cited by 24
Cited by15
Results whose statement or proof uses this declaration.
- IsCompactSystem.insert_univstatement and proof · cited by 2
- IsCompactSystem.monostatement and proof · cited by 2
- IsCompactSystem.of_nonempty_iInterstatement · cited by 2
- isCompactSystem_isCompact_isClosedstatement · cited by 2
- IsCompactSystem.iff_nonempty_iInterstatement · cited by 1
- IsCompactSystem.insert_emptystatement and proof · cited by 1
- IsCompactSystem.nonempty_iInterstatement and proof · cited by 1
- isCompactSystem_iff_of_directedstatement and proof · cited by 1
- isCompactSystem_insert_empty_iffstatement and proof · cited by 1
- IsCompactSystem.of_IsEmptystatement · cited by 0
- isCompactSystem_iff_nonempty_iInter_of_directedstatement · cited by 0
- isCompactSystem_iff_nonempty_iInter_of_ltstatement · cited by 0