Theorems · Theorem · general topology
isCompactSystem_insert_univ_iff
∀ {α : Type u_1} {S : Set (Set α)}, IsCompactSystem (insert Set.univ S) ↔ IsCompactSystem SA set system is a compact system iff adding univ gives a compact system.
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- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
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.univstatement and proof · cited by 3,945
- Set.subset_insertproof · cited by 96
- IsCompactSystemstatement and proof · cited by 15
- IsCompactSystem.insert_univproof · cited by 2
- IsCompactSystem.monoproof · cited by 2
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