Theorems · Theorem · algebraic geometry
IsRetrocompact.finsetInf
∀ {X : Type u_2} [inst : TopologicalSpace X] [T2Space X] {ι : Type u_4} {s : Finset ι} {t : ι → Set X},
(∀ i ∈ s, IsRetrocompact (t i)) → IsRetrocompact (s.inf t)- Defined in
- Mathlib.Topology.Constructible
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- T2Spacestatement and proof · cited by 1,351
- Finset.consproof · cited by 221
- Finset.infstatement and proof · cited by 219
- Finset.cons_inductionproof · cited by 85
- IsRetrocompactstatement and proof · cited by 43
- Finset.inf_consproof · cited by 16
- Finset.inf_emptyproof · cited by 15
- Finset.forall_of_forall_consproof · cited by 5
- IsRetrocompact.interproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsRetrocompact.finsetInf'proof · cited by 0