The function $f : \mathbb { R } ^ { n } \rightarrow \mathbb { R }$, defined as $f \left( x _ { 1 } , \cdots , x _ { n } \right) = \operatorname { Max } \left\{ \left| x _ { i } \right| \right\} , i = 1 , \cdots , n$, is uniformly continuous.
The function $f : \mathbb { R } ^ { n } \rightarrow \mathbb { R }$, defined as $f \left( x _ { 1 } , \cdots , x _ { n } \right) = \operatorname { Max } \left\{ \left| x _ { i } \right| \right\} , i = 1 , \cdots , n$, is uniformly continuous.