Theorems · Definition · general topology
TopologicalSpace.NoetherianSpace
(α : Type u_1) → [TopologicalSpace α] → Prop
Type class for Noetherian spaces. It is defined to be spaces whose open sets satisfies ACC.
- Defined in
- Mathlib.Topology.NoetherianSpace
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- TopologicalSpace.Opensproof · cited by 2,040
- WellFoundedGTproof · cited by 114
Cited by23
Results whose statement or proof uses this declaration.
- TopologicalSpace.NoetherianSpace.isCompactstatement and proof · cited by 5
- TopologicalSpace.noetherianSpace_iff_opensstatement · cited by 3
- TopologicalSpace.NoetherianSpace.finite_irreducibleComponentsstatement and proof · cited by 3
- TopologicalSpace.noetherianSpace_iff_of_homeomorphstatement and proof · cited by 2
- TopologicalSpace.noetherianSpace_of_surjectivestatement and proof · cited by 2
- TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreduciblestatement and proof · cited by 2
- TopologicalSpace.NoetherianSpace.of_subsetstatement and proof · cited by 2
- TopologicalSpace.noetherianSpace_TFAEstatement and proof · cited by 1
- TopologicalSpace.noetherianSpace_iff_isCompactstatement and proof · cited by 1
- TopologicalSpace.NoetherianSpace.exists_finite_set_isClosed_irreduciblestatement and proof · cited by 1
- AlgebraicGeometry.noetherianSpace_of_isAffinestatement · cited by 1
- Topology.IsInducing.noetherianSpacestatement and proof · cited by 1