\begin{definition}[Definition:Asymptotically Equal/General Definition/Point]
Let $T = \left({S, \tau}\right)$ be a topological space.
Let $V$ be a normed vector space over $\R$ or $\C$ with norm $\left\Vert{\, \cdot \,}\right\Vert$.
Let $f, g: S \to V$ be mappings.
Let $x_0 \in X$.
Then:
: $f$ is '''asymptotically equal''' to $g$ as $x \to x_0$
{{iff}}:
: $f - g = o \left({g}\right)$ as $x \to x_0$
where $o$ denotes little-O notation.
Category:Definitions/Asymptotic Notation
\end{definition}