1 files changed, 9 insertions, 5 deletions
diff --git a/library/topology/preclosure.tex b/library/topology/preclosure.tex
index 6c104be..e9ed27f 100644
--- a/library/topology/preclosure.tex
+++ b/library/topology/preclosure.tex
@@ -1,18 +1,22 @@
 \import{set.tex}
+\import{function.tex}
 
 \section{Preclosure spaces}
 
 
-\begin{struct}
+\begin{struct}\label{preclosure_space}
     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 $\cl(A\union B) = \cl(A) \union \cl(B)$.
+        \item\label{preclosure_type} For all $Y\subseteq\carrier[X]$ we have
+            $\cl[X](Y)\subseteq\carrier[X]$.
+        \item\label{preclosure_empty} $\cl[X](\emptyset)=\emptyset$.
+        \item\label{preclosure_extensive} For all $A\subseteq\carrier[X]$ we have
+            $A\subseteq\cl[X](A)$.
+        \item\label{preclosure_union} For all $A,B\subseteq\carrier[X]$ we have
+            $\cl[X](A\union B)=\cl[X](A)\union\cl[X](B)$.
     \end{enumerate}
 \end{struct}