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How to write the following mathematical expression in LaTeX? enter image description here

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    What is your particular doubt? Do you know the basics of (La)TeX? What have you done so far? Could you add some minimal base code to help the other users start from something rather that start with a plain blank file. – Manuel May 11 '17 at 13:09
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    The braced part can be done with cases from amsmath, see tex.stackexchange.com/questions/32140/… – Torbjørn T. May 11 '17 at 13:10
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There are errors in the original, which I have tried to correct.

\documentclass{amsart}
\begin{document}
\[
f^+_A \tilde{\circ} g_A^+ \colon S \longrightarrow P(U), x \longmapsto
\begin{cases}
\bigcup_{x=pq} \left\{f_A^+(p) \cap g_A^+(q)\right\}, & \text{ if \(\exists p,q \in S\) such that \(x=pq\)},
\emptyset, & \text{otherwise}
\end{cases}
\]
\end{document}

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