ThmDex – An index of mathematical definitions, results, and conjectures.
P1392
Result R50: Set difference equals intersection with complement shows that \begin{equation} F \setminus U = F \cap (X \setminus U) \end{equation} The complement $X \setminus U$ is closed in $T$ since $U$ is open in $T$, whence R75: Intersection of closed sets is closed implies the result. $\square$