Fixed regex incident.

src/topology/main/baire.tex

@@ -9,7 +9,7 @@
         \item For any $\seq{A_n} \subset 2^X$ nowhere dense, $\bigcup_{n \in \nat^+}A_n \subsetneq X$.
         \item For any $\seq{A_n} \subset 2^X$ closed with empty interior, $\bigcup_{n \in \nat^+}A_n$ has empty interior.
         \item For any $\seq{U_n} \subset 2^X$ open and dense, $\bigcap_{n \in \nat^+}U_n$ is dense.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $X$ is a \textbf{Baire space}.
 \end{definition}
@@ -29,7 +29,7 @@
     \begin{enumerate}
         \item[(a)] For all $n > 1$, $\ol V_n \subset U_n \cap V_{n - 1} \subset U$.
         \item[(b)] $\bigcap_{j \in \natp} \ol V_j$ is non-empty.
-    \end\{enumerate\}
+    \end{enumerate}
 
     then $X$ is a Baire space.
 \end{lemma}

src/topology/main/compact.tex

@@ -9,7 +9,7 @@
         \item For every family $\seqi{E}$ of closed sets with $\bigcap_{j \in J}E_j \ne \emptyset$ for all $J \subset I$ finite, $\bigcap_{i \in I}E_i \ne \emptyset$.
         \item Every filter in $X$ has a cluster point.
         \item Every ultrafilter in $X$ converges.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $X$ is \textbf{compact}.
 \end{definition}
@@ -90,7 +90,7 @@
     \begin{enumerate}
         \item For any $x \in X$ and $U \in \cn_{X \times Y}^o(\bracs{x} \times Y)$, there exists $V \in \cn_X(x)$ such that $V \times Y \subset U$. 
         \item For any $A \subset X$ and $U \in \cn_{X \times Y}^o(A \times Y)$, there exists $V \in \cn_X(A)$ such that $V \times Y \subset U$. 
-    \end\{enumerate\}
+    \end{enumerate}
 
     
 \end{lemma}

src/topology/main/connected.tex

@@ -8,7 +8,7 @@
         \item For any $\emptyset \ne U, V \subset X$ open with $U \cup V = X$, $U \cap V \ne \emptyset$.
         \item There exists no surjective $f \in C(X; \bracs{0, 1})$.
         \item For any $U \subset X$ open and closed, either $U = \emptyset$ or $U = X$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $X$ is \textbf{connected}.
 \end{definition}

src/topology/main/continuity.tex

@@ -8,7 +8,7 @@
     \begin{enumerate}
         \item For each $V \in \cn(f(x))$, $f^{-1}(V) \in \cn(x)$.
         \item For each filter base $\fB \subset 2^X$ converging to $x$, $f(\fB)$ converges to $f(x)$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $f$ is \textbf{continuous at} $x \in X$.
 
@@ -17,7 +17,7 @@
         \item For each $U \subset Y$ open, $f^{-1}(U)$ is open in $X$.
         \item $f$ is continuous at every $x \in X$.
         \item For each convergent filter base $\fB \subset 2^X$, $f(\fB)$ is convergent.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $f$ is \textbf{continuous}.
 
@@ -41,7 +41,7 @@
     \begin{enumerate}
         \item[(a)] $\bigcup_{i \in I}U_i = X$.
         \item[(b)] For each $i, j \in I$, either $U_i \cap U_j = \emptyset$, or $f_i|_{U_i \cap U_j} = f_j|_{U_i \cap U_j}$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     then there exists a unique $f \in C(X; Y)$ such that $f|_{U_i} = f_i$ for all $i \in I$.
 \end{lemma}

src/topology/main/filters.tex

@@ -25,7 +25,7 @@
     \begin{enumerate}
         \item[(FB1)] For any $E, F \in \fB$, there exists $G \in \fB$ such that $G \subset E \cap F$.
         \item[(FB2)] $\emptyset \not\in \fB$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     Conversely, if $\fB \subset 2^X$ is a non-empty collection that satisfies (FB1) and (FB2), then $\fB$ is a base for the filter
     \[
@@ -53,7 +53,7 @@
     \begin{enumerate}
         \item $f(\fB) = \bracs{f(E)| E \in \fB}$ is also a filter base.
         \item If $\fB$ is an ultrafilter base, then $f(\fB)$ is also an ultrafilter base. 
-    \end\{enumerate\}
+    \end{enumerate}
 
     
 \end{proposition}
@@ -119,7 +119,7 @@ The smallest filter $\fF(\fB_0) \subset 2^X$ containing $\fB_0$ is the filter \t
         \item $\fF$ is maximal with respect to inclusion.
         \item For any $E \subset X$, either $E \in \fF$ or $E^c \in \fF$.
         \item For any $\seqf{F_j} \subset X$ such that $\bigcup_{j = 1}^n F_j \in \fF$, there exists $1 \le j \le n$ such that $F_j \in \fF$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $\fF$ is an \textbf{ultrafilter}.
 \end{definition}
@@ -160,7 +160,7 @@ The smallest filter $\fF(\fB_0) \subset 2^X$ containing $\fB_0$ is the filter \t
         \item $\fF \supset \cn(x)$.
         \item For each ultrafilter $\fU \supset \fF$, $\fU \supset \cn(x)$.
         \item There exists a fundamental system of neighbourhoods $\cb(x) \subset \cn(x)$ such that for every $E \in \cb$, there exists $F \in \fB$ with $F \subset E$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $x$ is a \textbf{limit point} of $\fB$, and $\fB$ \textbf{converges} to $x$.
 
@@ -182,7 +182,7 @@ The smallest filter $\fF(\fB_0) \subset 2^X$ containing $\fB_0$ is the filter \t
         \item $x \in \bigcap_{E \in \fF}\overline{E}$.
         \item There exists a fundamental system of neighbourhoods $\cb(x) \subset \cn(x)$ such that for every $E \in \cb$ and $f \in \fB$, $E \cap F \ne \emptyset$.
         \item There exists a filter $\fU \supset \fB$ that converges to $x$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $x$ is a \textbf{cluster/accumulation point} of $\fB$. In particular, if $\fF$ is an ultra filter, then (6) implies that the limit points and cluster points of $\fF$ coincide.
 \end{definition}

src/topology/main/hausdorff.tex

@@ -12,7 +12,7 @@
         \item Every filter in $X$ converges to at most one point.
         \item For any index set $I$, the diagonal $\Delta$ is closed in $X^I$.
         \item The diagonal $\Delta$ is closed in $X \times X$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $X$ is a \textbf{T2/Hausdorff} space.
 \end{definition}

src/topology/main/lch.tex

@@ -8,7 +8,7 @@
         \item For any $x \in X$, there exists $K \in \cn(x)$ compact.
         \item For any $x \in X$, $\cn(x)$ admits a fundamental system of neighbourhoods consisting of compact sets.
         \item For any $x \in X$, $\cn(x)$ admits a fundamental system of neighbourhoods consisting of precompact sets.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $X$ is a \textbf{locally compact Hausdorff (LCH)} space.
 \end{definition}
@@ -122,7 +122,7 @@
         \item[(a)] For each $0 \le k \le n$, $U_k$ is a precompact open set.
         \item[(b)] For each $0 \le k < n$, $\overline{U_k} \subset U_{k+1}$.
         \item[(c)] For each $1 \le k \le n$, $U_k \supset \bigcup_{j = 1}^k K_j$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     By \autoref{lemma:lch-compact-neighbour}, there exists $U_{n+1} \in \cn^o(\overline{U_n} \cup K_{n+1})$ precompact. In which case, by (c),
     \[
@@ -185,7 +185,7 @@
     \begin{enumerate}
         \item[(a)] $\ol{E} \subset \bigcup_{x \in X_E}N_x$.
         \item[(b)] For every $x \in X_E$, $N_x \cap E \ne \emptyset$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     Let $X_{\ce} = \bigcup_{E \in \ce}X_\ce$, and for each $E \in \ce$, let
     \[

src/topology/main/neighbourhoods.tex

@@ -36,13 +36,13 @@
         \item[(F2)] For any $A, B \in \cn_\topo(x)$, $A \cap B \in \cn_\topo(x)$.
         \item[(V1)] For every $A \in \cn_\topo(x)$, $x \in A$.
         \item[(V2)] For every $V \in \cn_\topo(x)$, there exists $W \in \cn_\topo(x)$ such that $V \in \cn_\topo(y)$ for all $y \in W$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     Conversely, if $\cn: X \to 2^X$ is a mapping such that
     \begin{enumerate}
         \item $\cn(x) \ne \emptyset$ for all $x \in X$.
         \item $\cn(x)$ satisfies (F1), (F2), (V1), and (V2).
-    \end\{enumerate\}
+    \end{enumerate}
 
     then there exists a unique topology $\topo \subset 2^X$ such that $\cn = \cn_\topo$.
 \end{proposition}

src/topology/main/normal.tex

@@ -23,7 +23,7 @@
         \begin{enumerate}
             \item[(a)] $U_1 = B^c$.
             \item[(b)] For any $p, q \in \rational \cap [0, 1]$ with $p < q$, $\overline{U_p} \subset U_q$.
-        \end\{enumerate\}
+        \end{enumerate}
 
         \item There exists $f \in C(X; [0, 1])$ with $f|_A = 0$ and $f|_B = 1$.
     \end{enumerate}

src/topology/main/quotient.tex

@@ -12,7 +12,7 @@
     \begin{enumerate}
         \item For any $U \subset Y$, $U$ is open if and only if $\pi^{-1}(U)$ is open.
         \item $\pi \in C(X; Y)$, and for any $U \subset X$ saturated and open, $\pi(U)$ is open.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If the above holds, then $\pi$ is a \textbf{quotient map}.
 \end{definition}
@@ -38,7 +38,7 @@
         \]
 
         \item $\pi$ is a quotient map.
-    \end\{enumerate\}
+    \end{enumerate}
 
     The space $(\td X, \pi)$ is the \textbf{quotient} of $X$ by $\sim$.
 \end{definition}

src/topology/main/regular.tex

@@ -7,7 +7,7 @@
     \begin{enumerate}
         \item For each $x \in X$ and $A \subset X$ closed with $x \not\in A$, there exists $U \in \cn(x)$ and $V \in \cn(A)$ such that $U \cap V = \emptyset$.
         \item For each $x \in X$, the closed neighbourhoods of $x$ forms a fundamental system of neighbourhoods at $x$.
-    \end\{enumerate\}
+    \end{enumerate}
 
     If $X$ is a T1 space such that the above holds, then $X$ is \textbf{regular}.
 \end{definition}