Theorems · Theorem · general topology
TopologicalSpace.Opens.coe_finset_inf
∀ {ι : Type u_1} {α : Type u_2} [inst : TopologicalSpace α] (f : ι → TopologicalSpace.Opens α) (s : Finset ι),
↑(s.inf f) = s.inf (SetLike.coe ∘ f)- Defined in
- Mathlib.Topology.Sets.Opens
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- Finset.infstatement · cited by 219
- map_finset_infproof · cited by 10
- TopologicalSpace.Opens.coe_infproof · cited by 3
- TopologicalSpace.Opens.coe_topproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.exists_lift_of_germInjective_auxproof · cited by 1