Theorems · Definition · general topology
topologicalKrullDim
(T : Type u_1) → [TopologicalSpace T] → WithBot ℕ∞
The Krull dimension of a topological space is the supremum of lengths of chains of closed irreducible sets.
- Defined in
- Mathlib.Topology.KrullDimension
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- ENatstatement · cited by 4,985
- WithBotstatement · cited by 1,498
- Order.krullDimproof · cited by 82
- TopologicalSpace.IrreducibleClosedsproof · cited by 30
Cited by6
Results whose statement or proof uses this declaration.
- Topology.IsInducing.topologicalKrullDim_lestatement · cited by 2
- AlgebraicGeometry.IsLocallyArtinian.of_topologicalKrullDim_le_zerostatement and proof · cited by 2
- topologicalKrullDim_zero_of_discreteTopologystatement · cited by 2
- PrimeSpectrum.topologicalKrullDim_eq_ringKrullDimstatement · cited by 1
- IsHomeomorph.topologicalKrullDim_eqstatement and proof · cited by 1
- topologicalKrullDim_subspace_lestatement · cited by 1