noncomputable def noetherianTopologicalDim (X : Type u_1) [TopologicalSpace X] [TopologicalSpace.NoetherianSpace X] : WithBot ℕ∞

Lecture 4, Definition 11: the dimension of a Noetherian topological space, defined as the topological Krull dimension (the supremum of lengths of chains of irreducible closed subsets).

theorem noetherianTopologicalDim_eq_krullDim (X : Type u_1) [TopologicalSpace X] [TopologicalSpace.NoetherianSpace X] : noetherianTopologicalDim X = Order.krullDim (TopologicalSpace.IrreducibleCloseds X)

The Noetherian topological dimension equals the Krull dimension of the poset of irreducible closed subsets.

theorem noetherianTopologicalDim_eq_topologicalKrullDim (X : Type u_1) [TopologicalSpace X] [TopologicalSpace.NoetherianSpace X] : noetherianTopologicalDim X = topologicalKrullDim X

The Noetherian topological dimension is, by definition, the topological Krull dimension.