Definition:Noetherian Topological Space/Definition 1

Definition

A topological space $T = \struct {S, \tau}$ is Noetherian if and only if its set of closed sets, ordered by the subset relation, satisfies the descending chain condition.

Also see

• Equivalence of Definitions of Noetherian Topological Space

Sources

• 1977: Robin Hartshorne: Algebraic Geometry $\text {I}.1:$ Affine Varieties