---- > [!definition] Definition. ([[saturated set]]) > Let $X, Y$ be [[topological space|topological spaces]] and $p:X \to Y$ a [[surjection]]. We say a subset $C \subset X$ is **saturated** with respect to $p$ if $C$ contains every fiber $p ^{-1}(\{ y \})$ that it intersects. Thus $C$ is saturated if $C=p ^{-1} (U)$ for some subset $U$ of $Y$. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```