To get a single left curly bracket use $\left\{\ldots\right.$. Any type of bracket supported by LaTeX in maths mode can replace the curly bracket. Note the full stop: this stops LaTeX adding that bracket. To get a single bracket on the right hand side, swap the bracket type and the full stop: $\left.\ldots\right\}$.
\documentclass[a4paper,12pt]{article}
\begin{document}
$\left\{\ldots\right.$
$\left.\ldots\right\}$
\end{document}
I can’t remember where I found this, but it was on a forum explaining how to do one bracket with multiple lines of text inside it.
