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+\import{set.tex}
+
+\section{Preclosure spaces}
+
+
+\begin{struct}
+    A preclosure space $X$ is a onesorted structure equipped with
+    \begin{enumerate}
+        \item $\cl$
+    \end{enumerate}
+    such that
+    \begin{enumerate}
+        \item For all $Y\subseteq X$ we have $\cl(Y)\subseteq X$.
+        \item $\cl(\emptyset) = \emptyset$.
+        \item For all $A$ we have $A\subseteq \cl(A)$.
+        \item For all $A, B$ we have $\cl(A\union B) = \cl(A) \union \cl(B)$.
+    \end{enumerate}
+\end{struct}