document class: report
\[
f(x)=
\begin{cases}
1 &\text{if } x\in U\\
F(x) &\text{if } x\notin U.
\end{cases}
\]
If $T$ is open in $[0,1]$ then
\[
f^{-1}[T]=\begin{cases}
\big(F^{-1}[T]\cap X\big)\cup U &\text{if } 1\in T\\
F^{-1}[T]\cap V &\text{if } 1\notin T,
\end{cases}
\]
This produces
Does anyone else think the brackets look a little too big? How can I correct this?
EDIT: I believe the problem is that \doublespace is used throughout the document. (I was able to replicate the image using that). \linespread{1} made the brackets smaller, but it only seems to work if it's outside of the proof environment (and then it shrinks everything!).



\renewcommand{\arraystretch}{<num>}somewhere in your preamble? – Werner Apr 06 '17 at 23:30