---
date: 2022-03-30 20:46
modification date: Wednesday 30th March 2022 20:46:06
title: "quasicompact"
aliases: [quasicompact]

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Last modified date: <%+ tp.file.last_modified_date() %>


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- Tags 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [quasiseparated](Unsorted/separated.md)

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# quasicompact


- A space $X\in \Top$ is **quasicompact** iff every open cover admits a finite subcover.
- A morphism $f\in \Sch(X, Y)$ is quasicompact iff $Y$ admits an affine open cover $\mcv \covers Y$ with $f\inv(\mcv)$ all quasicompact spaces.

- A morphism is **quasicompact** if it sends [quasicompact](quasicompact.md) sets to quasicompact sets.