\begin{definition}[Definition:Oscillation/Real Space/Oscillation at Point/Infimum]
Let $X$ and $Y$ be real sets.
Let $f: X \to Y$ be a real function.
Let $x \in X$.
Let $\NN_x$ be the set of neighborhoods of $x$.
The '''oscillation of $f$ at $x$''' is defined as:
:$\ds \map {\omega_f} x := \inf_{U \mathop \in \NN_x} \map {\omega_f} {U \cap X}$
where $\map {\omega_f} {U \cap X}$ denotes the oscillation of $f$ on $U \cap X$.
\end{definition}