---
date: 2022-01-15 21:49
modification date: Friday 28th January 2022 17:50:39
title: quaiseparated
aliases: [quaiseparated]

---

Tags: 
#AG 
Refs:
[stacks MOC](Unsorted/stacks%20MOC.md)
[scheme](Unsorted/scheme.md)

# quaiseparated

A **morphism** $f:X\to Y$ is quasiseparated iff  $\Delta_Y: X\to X\fiberprod{Y}X$ is quasicompact, so inverse images of quasicompact sets are again quasicompact. 

A **scheme** is quasiseparated iff its structure morphism $X\to \spec \ZZ$ is quasiseparated.

This is weaker than being a [separated](Unsorted/separated.md) morphism.

# Examples

The line with two origins is quasiseparated but not [separated](separated.md).