Theorems · Inductive type · general topology
TopologicalSpace.Closeds
(α : Type u_4) → [TopologicalSpace α] → Type u_4
The type of closed subsets of a topological space.
- Defined in
- Mathlib.Topology.Sets.Closeds
- Cited by
- 168 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · 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 by191
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.supportstatement · cited by 40
- TopologicalSpace.NonemptyCompacts.toClosedsstatement · cited by 15
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdealstatement and proof · cited by 13
- TopologicalSpace.Compacts.toClosedsstatement · cited by 12
- TopologicalSpace.Closeds.closurestatement · cited by 11
- TopologicalSpace.Closeds.complstatement and proof · cited by 10
- AlgebraicGeometry.Scheme.IdealSheafData.gcstatement and proof · cited by 8
- TopologicalSpace.Opens.complstatement · cited by 8
- TopologicalSpace.Closeds.isClosedstatement and proof · cited by 7
- TopologicalSpace.Closeds.extstatement and proof · cited by 6
- TopologicalSpace.Closeds.isUniformEmbedding_coestatement · cited by 6
- AlgebraicGeometry.Scheme.IdealSheafData.coe_support_interstatement · cited by 6