---- > [!definition] Definition. ([[uniformly bounded]]) > Let $X$ be a set and let $(Y,d)$ be a [[metric space]]. A family of functions $f_{i}:X \to Y$, $i \in I$, is called **uniformly bounded** if there exists $a \in Y$ and $M \geq 0$ such that $d\big( f_{i}(x), a \big) \leq M \text{ for all }i \in I \text{ and for all } x \in X.$ ---- #### ---- #### 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 > ```