Definition:Noetherian Topological Space/Definition 4

Definition

A topological space $T = \struct {S, \tau}$ is Noetherian if and only if each non-empty set of open sets has a maximal element with respect to the subset relation.

Also see

• Equivalence of Definitions of Noetherian Topological Space

Sources

• 1977: Robin Hartshorne: Algebraic Geometry Exercise $\text {I}.1.7 \paren a$