\begin{definition}[Definition:Continuous Total Preordering]
Let $S$ be a set.
Let $\precsim$ be a total preordering on $S$.
Let $\precsim$ be such that:
:$a \precsim b$ whenever there exist sequences $\left\langle{a^k}\right\rangle_k$ and $\left\langle{b^k}\right\rangle_k$ that converge to $a$ and $b$ respectively for which $a^k \precsim b^k$ for all $k$.
Then $\precsim$ is '''continuous'''.
{{explain|The above has been rendered more-or-less verbatim from the source cited, but it is not well explained. Its context appears to be important in the discipline of game theory.}}
\end{definition}