\begin{definition}[Definition:Compact Absolute Convergence]
Let $X$ be a topological space.
Let $\struct {V, \norm {\, \cdot \,} }$ be a normed vector space.
Let $\sequence {f_n}$ be a sequence of mappings $f_n: X \to V$.
Then the series $\ds \sum_{n \mathop = 1}^\infty f_n$ '''converges compactly (uniformly) absolutely''' {{iff}} the series $\ds \sum_{n \mathop = 1}^\infty \norm {f_n}$ converges compactly.
\end{definition}