Theorems · Theorem · general topology
JacobsonSpace.closure_inter_closedPoints_eq_closure
∀ {X : Type u_1} [inst : TopologicalSpace X] [JacobsonSpace X] {S : Set X},
IsLocallyClosed S → closure (S ∩ closedPoints X) = closure S- Defined in
- Mathlib.Topology.JacobsonSpace
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- closurestatement and proof · cited by 1,254
- LE.le.antisymmproof · cited by 507
- Set.inter_subset_leftproof · cited by 360
- subset_closureproof · cited by 309
- isClosed_closureproof · cited by 195
- closure_monoproof · cited by 133
- IsClosed.isOpen_complproof · cited by 126
- IsClosed.closure_subset_iffproof · cited by 59
- IsLocallyClosedstatement and proof · cited by 44
- closedPointsstatement and proof · cited by 25
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ext_of_apply_eqproof · cited by 1
- subsingleton_image_closure_of_finite_of_isPreirreducibleproof · cited by 1