Theorems · Theorem · general topology
TopologicalSpace.Compacts.isCompact_biUnion_coe_of_isCompact
∀ {α : Type u_1} [inst : TopologicalSpace α] {S : Set (TopologicalSpace.Compacts α)},
IsCompact S → IsCompact (⋃ K ∈ S, ↑K)- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 2 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.
Cites22
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.coestatement and proof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- LE.le.transproof · cited by 3,151
- Set.iUnionstatement and proof · cited by 2,483
- IsOpenproof · cited by 2,400
- IsCompactstatement and proof · cited by 1,282
- TopologicalSpace.Compactsstatement and proof · cited by 386
- Finset.biUnionproof · cited by 217
- Set.mem_iUnionproof · cited by 212
Cited by2
Results whose statement or proof uses this declaration.
- TopologicalSpace.NonemptyCompacts.isCompact_biUnion_coe_of_isCompactproof · cited by 2
- TopologicalSpace.Compacts.compactSpace_iffproof · cited by 0