\begin{definition}[Definition:Locally Uniform Convergence/Series]
Let $X$ be a topological space.
Let $V$ 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 locally uniformly''' {{iff}} the sequence of partial sums converges locally uniformly.
Category:Definitions/Uniform Convergence
\end{definition}