Lemma 26.11.4. The underlying topological space of any scheme is locally quasi-compact, see Topology, Definition 5.13.1.

Proof. This follows from Lemma 26.11.2 above and the fact that the spectrum of ring is quasi-compact, see Algebra, Lemma 10.16.10. $\square$

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).