Theorems · Theorem · general topology
TopologicalSpace.IsOpenCover.jacobsonSpace_iff
∀ {X : Type u_2} [inst : TopologicalSpace X] {ι : Type u_1} {U : ι → TopologicalSpace.Opens X},
TopologicalSpace.IsOpenCover U → (JacobsonSpace X ↔ ∀ (i : ι), JacobsonSpace ↥(U i))- Defined in
- Mathlib.Topology.JacobsonSpace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 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.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.Nonemptyproof · cited by 2,627
- Set.extproof · cited by 2,266
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- IsClosedproof · cited by 1,639
- Set.image_singletonproof · cited by 174
- continuous_subtype_valproof · cited by 159
- TopologicalSpace.Opens.is_open'proof · cited by 139
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpaceproof · cited by 2