Theorems · Definition · general topology
closedPoints
(X : Type u_1) → [TopologicalSpace X] → Set X
The set of closed points.
- Defined in
- Mathlib.Topology.JacobsonSpace
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.ofPredproof · cited by 6,101
- IsClosedproof · cited by 1,639
Cited by28
Results whose statement or proof uses this declaration.
- nonempty_inter_closedPointsstatement · cited by 5
- jacobsonSpace_iff_locallyClosedstatement and proof · cited by 4
- AlgebraicGeometry.pointEquivClosedPointstatement and proof · cited by 4
- isClosed_singleton_of_isLocallyClosed_singletonproof · cited by 3
- JacobsonSpace.of_isOpenEmbeddingproof · cited by 3
- PrimeSpectrum.isJacobsonRing_iff_jacobsonSpaceproof · cited by 2
- JacobsonSpace.closure_inter_closedPointsstatement · cited by 2
- JacobsonSpace.closure_inter_closedPoints_eq_closurestatement and proof · cited by 2
- mem_closedPoints_iffstatement · cited by 2
- AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPointsstatement and proof · cited by 1
- Topology.IsClosedEmbedding.preimage_closedPointsstatement · cited by 1