Theorems · Inductive type · general topology
JacobsonSpace
(X : Type u_1) → [TopologicalSpace X] → Prop
The class of Jacobson spaces, i.e. spaces such that the set of closed points are dense in every closed subspace.
- Defined in
- Mathlib.Topology.JacobsonSpace
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by22
Results whose statement or proof uses this declaration.
- nonempty_inter_closedPointsstatement and proof · cited by 5
- jacobsonSpace_iff_locallyClosedstatement · cited by 4
- isClosed_singleton_of_isLocallyClosed_singletonstatement and proof · cited by 3
- JacobsonSpace.of_isOpenEmbeddingstatement and proof · cited by 3
- PrimeSpectrum.isJacobsonRing_iff_jacobsonSpacestatement and proof · cited by 2
- AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpacestatement and proof · cited by 2
- JacobsonSpace.closure_inter_closedPointsstatement and proof · cited by 2
- JacobsonSpace.closure_inter_closedPoints_eq_closurestatement and proof · cited by 2
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpacestatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPointsstatement and proof · cited by 1
- closure_closedPointsstatement and proof · cited by 1