Book keeping.

src/cat/gluing/level.tex

@@ -1,7 +1,7 @@
 \section{Preimages}
 \label{section:preimage}
 
-\begin{definition}[Preimage Function]
+\begin{definition}[Preimage Function*]
 \label{definition:preimage-function}
     Let $X, Y$ be sets and $P: 2^Y \to 2^X$, then $P$ is a \textbf{preimage function} if
     \begin{enumerate}[label=(PF\arabic*)]
@@ -20,7 +20,7 @@
 \label{proposition:preimage-gymnastics}
     Let $X$ and $Y$ be sets, then:
     \begin{enumerate}
-        \item For any $f: X \to Y$, the mapping $S \mapsto f^{-1}(S)$ is a total preimage function.
+        \item For any $f: X \to Y$, the mapping $S \mapsto f^{-1}(S)$ is a total \hyperref[preimage function]{definition:preimage-function}.
         \item For any total preimage function $P: 2^Y \to 2^X$, there exists a unique $f: X \to Y$ such that $P(S) = f^{-1}(S)$ for all $S \in 2^Y$. 
     \end{enumerate}
 \end{proposition}

src/measure/measurable-maps/approx.tex

@@ -1,7 +1,7 @@
 \section{Approximations with Simple Functions}
 \label{section:simple-approx}
 
-\begin{definition}[Admissible Approximant Function]
+\begin{definition}[Admissible Approximant Function*]
 \label{definition:admissible-approximant-function}
     Let $X$ be a topological space and $\mathcal{A}: X \to 2^X$, then $\mathcal{A}$ is an \textbf{admissible approximant function} on $X$ if:
     \begin{enumerate}[label=(AA\arabic*)]
@@ -21,7 +21,7 @@
 \end{lemma}
 
 
-\begin{definition}[Approximation of the Identity]
+\begin{definition}[Approximation of the Identity*]
 \label{definition:approximation-id-measure}
     Let $X$ be a topological space and $\net{I} \subset X^X$ be a net, then $\net{I}$ is an \textbf{approximation of the identity} if:
     \begin{enumerate}[label=(AI\arabic*)]

src/topology/main/preimage.tex

@@ -1,7 +1,7 @@
 \section{Open Preimage Functions}
 \label{section:preimage-function-topology}
 
-\begin{definition}[Open Preimage Function]
+\begin{definition}[Open Preimage Function*]
 \label{definition:open-preimage-function}
     Let $X$ be a set, $(Y, \topo)$ be a topological space, and $P: \topo \to 2^X$, then $P$ is an \textbf{open preimage function} if
     \begin{enumerate}[label=(PF\arabic*)]
@@ -15,7 +15,7 @@
 \label{proposition:open-preimage-function-gymnastics}
     Let $X$ be a set, $(Y, \topo)$ be a topological space, and $f: X \to Y$, then:
     \begin{enumerate}
-        \item The mapping $U \mapsto f^{-1}(U)$ is an open preimage function. 
+        \item The mapping $U \mapsto f^{-1}(U)$ is an \hyperref[open preimage function]{definition:open-preimage-function}. 
         \item If $Y$ is T1, then for any $g: X \to Y$ with $g^{-1}(U) = f^{-1}(U)$ for all $U \in \topo$, $f = g$. 
     \end{enumerate}
 \end{proposition}
@@ -29,7 +29,7 @@
 \end{proof}
 
 
-\begin{definition}[Basic Preimage Function]
+\begin{definition}[Basic Preimage Function*]
 \label{definition:basic-preimage-function}
     Let $X$ be a set, $Y$ be a topological space, $\mathcal{B}$ be a base for $Y$ with $\emptyset \in \mathcal{B}$, and $p: \mathcal{B} \to 2^X$, then $p$ is a \textbf{basic preimage function} if:
     \begin{enumerate}[label=(PF\arabic*)]
@@ -43,8 +43,8 @@
 \label{proposition:basic-preimage-function}
     Let $X$ be a set, $(Y, \topo)$ be a topological space, and $\mathcal{B}$ be a base for $Y$ with $\emptyset \in \mathcal{B}$, then:
     \begin{enumerate}
-        \item For any open preimage function $P: \topo \to 2^X$, $P|_{\mathcal{B}}$ is a basic preimage function.
-        \item For any basic preimage function $p: \mathcal{B} \to 2^X$, there exists a unique open preimage function $P: \topo \to 2^X$ such that $p = P|_{\mathcal{B}}$. 
+        \item For any \hyperref[open preimage function]{definition:open-preimage-function} $P: \topo \to 2^X$, $P|_{\mathcal{B}}$ is a basic preimage function.
+        \item For any \hyperref[basic preimage function]{definition:basic-preimage-function} $p: \mathcal{B} \to 2^X$, there exists a unique open preimage function $P: \topo \to 2^X$ such that $p = P|_{\mathcal{B}}$. 
     \end{enumerate}
 \end{proposition}
 \begin{proof}
@@ -84,7 +84,7 @@
 
 \begin{theorem}
 \label{theorem:open-preimage-function-existence}
-    Let $X$ be a set, $(Y, \fU)$ be a complete Hausdorff uniform space with topology $\topo$, and $P: \topo \to 2^X$ be an open preimage function such that:
+    Let $X$ be a set, $(Y, \fU)$ be a complete Hausdorff uniform space with topology $\topo$, and $P: \topo \to 2^X$ be an \hyperref[open preimage function]{definition:open-preimage-function} such that:
     \begin{enumerate}
         \item[(S)] For each $x \in X$ and $U \in \fU$, there exists a $U$-small set $V \in \topo$ such that $x \in P(V)$. 
     \end{enumerate}
@@ -106,7 +106,7 @@
 
 \begin{corollary}
 \label{corollary:basic-preimage-function-existence}
-    Let $X$ be a set, $(Y, \fU)$ be a complete Hausdorff uniform space, $\mathcal{B}$ be a base for $Y$ with $\emptyset \in \mathcal{B}$, and $p: \mathcal{B} \to 2^X$ be a basic preimage function such that:
+    Let $X$ be a set, $(Y, \fU)$ be a complete Hausdorff uniform space, $\mathcal{B}$ be a base for $Y$ with $\emptyset \in \mathcal{B}$, and $p: \mathcal{B} \to 2^X$ be a \hyperref[basic preimage function]{definition:basic-preimage-function} such that:
     \begin{enumerate}
         \item[(S')] For each $x \in X$ and $U \in \fU$, there exists a $U$-small set $V \in \mathcal{B}$ such that $x \in P(V)$. 
     \end{enumerate}