This diagram shows that the function f:R∖{0}→R:x↦{1x&gt;0−1x&lt;0{\displaystyle f:\mathbb {R} \setminus \{0\}\to \mathbb {R} :x\mapsto {\begin{cases}1&amp;x&gt;0\\-1&amp;x&lt;0\end{cases}}} is locally constant, i.e. for each argument there is a neighborhood where the function is constant.
Own work
Stephan Kulla (User:Stephan Kulla)