\begin{definition}[Definition:Outer Limit]
Let $\struct {X, \tau}$ be a Hausdorff topological space.
Let $\sequence {C_n}_{n \mathop \in \N}$ be a sequence of sets in $X$.
The '''outer limit''' of $\sequence {C_n}_{n \mathop \in \N}$ is defined as:
: $\ds \limsup_{n \mathop \to \infty} \ C_n := \set {x \in X: \exists N \text{ cofinal set of }\N, \exists x_v \in C_v \paren {v \in N} \text{ such that } x_v \to x}$
where $x_v \to x$ denotes convergence in the topology $\tau$.
\end{definition}