Theorems · Theorem · algebraic geometry
IsRetrocompact.finsetSup
∀ {X : Type u_2} [inst : TopologicalSpace X] {ι : Type u_4} {s : Finset ι} {t : ι → Set X},
(∀ i ∈ s, IsRetrocompact (t i)) → IsRetrocompact (s.sup t)- Defined in
- Mathlib.Topology.Constructible
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 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.
Cites11
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
- Finsetstatement and proof · cited by 13,712
- Finset.supstatement and proof · cited by 530
- Finset.consproof · cited by 221
- Finset.cons_inductionproof · cited by 85
- Finset.sup_emptyproof · cited by 72
- IsRetrocompactstatement and proof · cited by 43
- Finset.sup_consproof · cited by 30
- Finset.forall_of_forall_consproof · cited by 5
- IsRetrocompact.unionproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsRetrocompact.finsetSup'proof · cited by 0