Theorems · Theorem · general topology
isCompact_sInter_of_subset_constructibleTopologySubbasis
∀ {X : Type u_1} [inst : TopologicalSpace X] [CompactSpace X] [QuasiSeparatedSpace X] {s : Set (Set X)},
s ⊆ constructibleTopologySubbasis X → s.Finite → IsCompact (⋂₀ s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Set.ofPredproof · cited by 6,101
- Compl.complproof · cited by 2,925
- IsOpenproof · cited by 2,400
- Set.Finitestatement and proof · cited by 1,814
- IsClosedproof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- CompactSpacestatement and proof · cited by 593
- Set.sInterstatement · cited by 225
- QuasiSeparatedSpacestatement and proof · cited by 49
- constructibleTopologySubbasisstatement and proof · cited by 3
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