Tags: #AG Refs: stacks MOC scheme

quaiseparated

A morphism \(f:X\to Y\) is quasiseparated iff \(\Delta_Y: X\to X \underset{\scriptscriptstyle {Y} }{\times} X\) is quasicompact, so inverse images of quasicompact sets are again quasicompact.

A scheme is quasiseparated iff its structure morphism \(X\to \operatorname{Spec}{\mathbf{Z}}\) is quasiseparated.

This is weaker than being a separated morphism.

Examples

The line with two origins is quasiseparated but not separated.