From 7c66b227a494748e2a546fb85317accd00aebe53 Mon Sep 17 00:00:00 2001
From: Justin Gassner <justin.gassner@mailbox.org>
Date: Thu, 15 Feb 2024 05:11:07 +0100
Subject: Update

---
 pages/general-topology/topological-spaces.md | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

(limited to 'pages/general-topology/topological-spaces.md')

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
-
-
-- 
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