Large Curly brackets

Question

So I'm new to LaTeX and I have a problem. I want to type large curly brackets. My document type is article To be more specific, here's what I want to type:

Thank you all in advance.

Answer 1

Does this go in the right direction?

\documentclass[fleqn]{article}
\usepackage{amsmath,amsfonts}
\usepackage{newtxtext,newtxmath}
\begin{document}
\[\tau=\left\{ G\subset\overline{\mathfrak{R}}/ \forall x\in G,
\left\{\begin{array}{@{}l@{\ /\ }l@{,\ }l@{}}
\exists a,b\in\mathfrak{R} & x\in [a,b\mathclose[\subset G&x\ne\pm\infty\\
\exists b\in\mathfrak{R} & x\in [-\infty,b[\subset G&x=-\infty\\
\exists a\in\mathfrak{R} & x\in \mathopen]a,\infty]\subset G&x=+\infty
\end{array}\right\}
\right\}
\]
\end{document}

(I am not sure I understand the notation, though.) EDIT: Added \mathopen and \mathclose, as suggested by @egreg.)

Answer 2

Yet another solution, in two variants:

\documentclass{article}
\usepackage{array} 
\usepackage{mathtools}
\DeclarePairedDelimiter{\set} \{ \}

\DeclareFontFamily{U}{mathx}{\hyphenchar\font45}
\DeclareFontShape{U}{mathx}{m}{n}{
<-6> mathx5 <6-7> mathx6 <7-8> mathx7
<8-9> mathx8 <9-10> mathx9
<10-12> mathx10 <12-> mathx12
}{}
\DeclareSymbolFont{mathx}{U}{mathx}{m}{n}
\DeclareFontSubstitution{U}{mathx}{m}{n}
\DeclareMathAccent{\widebar}{0}{mathx}{"73}

\begin{document}

   \[ 
   \tau = \set*{%
   G \subset \widebar{\Re}\bigm / \forall X\in G, \begin{Bmatrix}
    \begin{array}{@{}l!{/}l@{\:}l@{}}
     \exists a, b \in\Re & x\in{]a, b[}\subset G, &x\ne \pm\infty \\
     \exists b \in\Re & x\in{[-\infty, b[}\subset G, &x = -\infty \\
     \exists ab \in\Re & x\in {]a, + \infty]} \subset G, &x = + \infty
    \end{array}
   \end{Bmatrix}}%
   \]%

   \[
   \tau = \set*{%
   G \subset \widebar{\Re}\bigm / \forall X\in G, \begin{cases}
    \begin{array}{@{}l!{/}l@{\:}l@{}}
     \exists a, b \in\Re & x\in{]a, b[}\subset G, &x\ne \pm\infty \\
     \exists b \in\Re & x\in{[-\infty, b[}\subset G, &x = -\infty \\
     \exists ab \in\Re & x\in {]a, + \infty]} \subset G, &x = + \infty
    \end{array}
   \end{cases}}%
   \]%

\end{document} 

Answer 3

Or maybe something like this? (Note that I've gone ahead and inserted commas as separators in the interval expressions.)

\documentclass{article}
\usepackage{amssymb} % for "\mathfrak" macro
\newcommand\R{\mathfrak{R}}

\begin{document}
\[
\tau=
\left\{
G\subset\overline{\R} \mid \forall x\in G,
\left\{
\begin{array}{@{}l@{}}
\exists a,b\in\R \mid 
   x\in\mathopen{]}a,b\mathclose{[} \subset G,\ x\ne\pm\infty \\
\exists b\in\R \mid
   [-\infty,b\mathclose{[} \subset G,\ x=-\infty \\
\exists a\in\R \mid
   \mathopen{]}a,+\infty]  \subset G,\ x=+\infty
\end{array}
\right\}
\right\}     
\]
\end{document}