Lemma 5.12.14. A quasi-compact locally Noetherian space is Noetherian.

Proof. The conditions imply immediately that $X$ has a finite covering by Noetherian subsets, and hence is Noetherian by Lemma 5.9.4. $\square$

There are also:

• 2 comment(s) on Section 5.12: Quasi-compact spaces and maps

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).