4 files changed, 23 insertions, 19 deletions

diff --git a/pages/general-topology/compactness/index.md b/pages/general-topology/compactness/index.md
index 37e9b4d..6c2e274 100644
--- a/pages/general-topology/compactness/index.md
+++ b/pages/general-topology/compactness/index.md
@@ -26,7 +26,8 @@ if and only if it has the following property:
   then there exists a finite subcollection of $\mathcal{O}$ that covers $X$.
 
 If $\mathcal{A}$ is a collection of subsets of $X$,
-let $\mathcal{A}^c = \braces{ X \setminus A : A \in \mathcal{A}}$ denote the collection of the complements of its members.
+let $\mathcal{A}^c = \braces{ X \setminus A : A \in \mathcal{A}}$ denote
+the collection of the complements of its members.
 Clearly, $\mathcal{B}$ is a subcollection of $\mathcal{A}$
 if and only if $\mathcal{B}^c$ is a subcollection of $\mathcal{A}^c$.
 Moreover, note that $\mathcal{B}$ covers $X$ if and only if
@@ -43,4 +44,3 @@ if and only if $\mathcal{A}^c$ consists of closed subsets of $X$.
 {% definition Finite Intersection Property%}
 TODO
 {% enddefinition %}
-
diff --git a/pages/general-topology/continuity-and-convergence.md b/pages/general-topology/continuity-and-convergence.md
index 7ae4534..57e5ca9 100644
--- a/pages/general-topology/continuity-and-convergence.md
+++ b/pages/general-topology/continuity-and-convergence.md
@@ -1,5 +1,5 @@
 ---
-title: Continuity & Convergence
+title: Continuity & Convergence
 parent: General Topology
 nav_order: 2
 ---
diff --git a/pages/general-topology/metric-spaces/index.md b/pages/general-topology/metric-spaces/index.md
index c0dc45a..52b2b4c 100644
--- a/pages/general-topology/metric-spaces/index.md
+++ b/pages/general-topology/metric-spaces/index.md
@@ -46,13 +46,13 @@ Clearly, a metric subspace of a metric space is itself a metric space.
 {% proposition %}
 Let $(X,d)$ be a (semi-)metric space.
 - For all $x,y,z \in X$ we have the *inverse triangle inequality*
-  
+
   $$
   \abs{d(x,y) - d(y,z)} \le d(x,z).
   $$
 
 - For all $v,w,x,y \in X$ we have the *quadrilateral inequality*
-  
+
   $$
   \abs{d(v,w) - d(x,y)} \le d(v,x) + d(w,y)
   $$
@@ -141,27 +141,31 @@ every sequence in $X$ has at most one limit.
 Let $(X,d_X)$ and $(Y,d_Y)$ be metric spaces.
 A mapping $f: X \to Y$ is called
 - *continuous at a point $x \in X$* if
-  
+
   $$
-  \forall\epsilon>0 \ \ \exists\delta>0 \ \ \forall x' \in X : \big\lparen d_X(x,x') \le \delta \implies d_Y(f(x),f(x')) < \epsilon \big\rparen
+  \forall\epsilon>0 \ \ \exists\delta>0 \ \ \forall x' \in X :
+  \big\lparen d_X(x,x') \le \delta \implies d_Y(f(x),f(x')) < \epsilon \big\rparen
   $$
 
 - *continuous* if it is continuous at every point of $X$, that is
-  
+
   $$
-  \forall x \in X \ \ \forall\epsilon>0 \ \ \exists\delta>0 \ \ \forall x' \in X : \big\lparen d_X(x,x') \le \delta \implies d_Y(f(x),f(x')) < \epsilon \big\rparen
+  \forall x \in X \ \ \forall\epsilon>0 \ \ \exists\delta>0 \ \ \forall x' \in X :
+  \big\lparen d_X(x,x') \le \delta \implies d_Y(f(x),f(x')) < \epsilon \big\rparen
   $$
 
 - *uniformly continuous* if
-  
+
   $$
-  \forall\epsilon>0 \ \ \exists\delta>0 \ \ \forall x,x' \in X : \big\lparen d_X(x,x') \le \delta \implies d_Y(f(x),f(x')) < \epsilon \big\rparen
+  \forall\epsilon>0 \ \ \exists\delta>0 \ \ \forall x,x' \in X :
+  \big\lparen d_X(x,x') \le \delta \implies d_Y(f(x),f(x')) < \epsilon \big\rparen
   $$
 
 - *Lipschitz continuous* if
-  
+
   $$
-  \exists L \ge 0 \ \ \forall x,x' \in X : d_Y(f(x),f(x')) \le L \, d_X(x,x') 
+  \exists L \ge 0 \ \ \forall x,x' \in X :
+  d_Y(f(x),f(x')) \le L \, d_X(x,x')
   $$
 {% enddefinition %}
 
diff --git a/pages/general-topology/topological-spaces.md b/pages/general-topology/topological-spaces.md
index b0b1834..cb0c30b 100644
--- a/pages/general-topology/topological-spaces.md
+++ b/pages/general-topology/topological-spaces.md
@@ -75,7 +75,8 @@ is the smallest topology on $X$ containing $\mathcal{A}$.
 
 {% definition Basis for a Topology %}
 A *basis for a topology* on a set $X$ is a collection $\mathcal{B}$ of subsets of $X$
-such that for every point $x \in X$ 
+such that for every point $x \in X$
+
 - there exists $B \in \mathcal{B}$ such that $x \in B$,
 - if $x \in B_1 \cap B_2$ for $B_1, B_2 \in \mathcal{B}$,
   then there exists a $B_3 \in \mathcal{B}$
@@ -85,6 +86,7 @@ such that for every point $x \in X$
 {% theorem Topology Generated by a Basis %}
 If $X$ is set and $\mathcal{B}$ is a basis for a topology on $X$,
 then the topology generated by $\mathcal{B}$ equals
+
 - the collection of all subsets $S \subset X$ with the property
   that for every $x \in S$ there exists a basis element $B \in \mathcal{B}$
   such that $x \in B$ and $B \subset S$;
@@ -125,7 +127,7 @@ then the topology generated by $\mathcal{S}$ equals
 Suppose $(X,\mathcal{T})$ is a topological space.
 A subset $S$ of $X$
 is called *open* with respect to $\mathcal{T}$
-when it belongs to $\mathcal{T}$
+when it belongs to $\mathcal{T}$,
 and it is called *closed* with respect to $\mathcal{T}$
 when its complement $X \setminus S$ belongs to $\mathcal{T}$.
 {% enddefinition %}
@@ -137,10 +139,8 @@ if and only if its complement is closed.
 Let $\mathcal{C}$ be the collection of closed subsets of a topological space. Then
 {: .mb-0 }
 - $X$ and $\varnothing$ belong to $\mathcal{C}$,
--  the intersection of any subcollection of $\mathcal{C}$ belongs to $\mathcal{C}$,
--  the union of any finite subcollection $\mathcal{C}$ belongs to $\mathcal{C}$.
+- the intersection of any subcollection of $\mathcal{C}$ belongs to $\mathcal{C}$,
+- the union of any finite subcollection $\mathcal{C}$ belongs to $\mathcal{C}$.
 {% endproposition %}
 
 ## The Subspace Topology
-
-