Definition:Noetherian Topological Space/Definition 2

Definition

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

Also see

• Equivalence of Definitions of Noetherian Topological Space

Sources

There is believed to be a mistake here, possibly a typo. In particular: Not all of these definitions can have been sourced from this item, surely? If so, chain them using the usual technique. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by reviewing it, and either correcting it or adding some explanatory material as to why you believe it is actually correct after all. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mistake}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

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