# quasicompact scheme are finite union of affine scheme

This is a problem from Liu`s book. Show that a scheme $X$ is quasi-compact if and only if it is a finite union of affine schemes. If the scheme is quasicompact then it is obviously a finite union of affine schemes. How to show the converse? Do we need that the affine schemes should be open in $X$?

• Yes, you should be thinking about affine open subschemes. – Zhen Lin Jun 1 '14 at 11:56
• Affine schemes are quasi-compact, isn't it? – awllower Jun 1 '14 at 14:33