From 46373a33ddaf1e5d1dcc167ecee9a716bb8af4fa Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Thu, 1 Jan 2026 19:30:10 +0100
Subject: [PATCH 1/4] Improve definition of S108

---
 spaces/S000108/README.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/spaces/S000108/README.md b/spaces/S000108/README.md
index 1df5c7a51..c604611ae 100644
--- a/spaces/S000108/README.md
+++ b/spaces/S000108/README.md
@@ -1,12 +1,12 @@
 ---
 uid: S000108
-name: Stone-Cech compactification of the integers
+name: Stone-Čech compactification of the integers
 aliases:
   - Beta N
   - βN
   - Beta Z
   - Beta omega
-  - Stone-Cech compactification of the natural numbers
+  - Stone-Čech compactification of the natural numbers
 counterexamples_id: 111
 refs:
   - zb: "0386.54001"
@@ -15,9 +15,9 @@ refs:
     name: Stone–Čech compactification on Wikipedia
 ---
 
-$\beta \omega$ is the set of all ultrafilters on $\omega=\{0,1,2\dots\}$,
-where we identify $n$ with the principal ultrafilter containing $n$.
-The topology on $\beta\omega$ is generated by all sets of the form
+The Stone-Čech compactification of {S2}. Explicitly, $X=\beta \omega$ is the set of all ultrafilters on $\omega=\{0,1,2\dots\}$,
+where we identify $n \in \omega$ with the principal ultrafilter containing $n$.
+The topology on $X$ is generated by all sets of the form
 $\overline U = \{F \in \beta\omega : U \in F\}$ for $U \subset \omega$.
 
 Defined as counterexample #111 ("Stone-Cech Compactification of the Integers")

From 4b86110015ed6e9cb1684356e60705b2faa67e4f Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Fri, 9 Jan 2026 23:15:52 +0100
Subject: [PATCH 2/4] apply prabau suggestions

---
 spaces/S000108/README.md | 8 ++------
 1 file changed, 2 insertions(+), 6 deletions(-)

diff --git a/spaces/S000108/README.md b/spaces/S000108/README.md
index c604611ae..f3088d9a7 100644
--- a/spaces/S000108/README.md
+++ b/spaces/S000108/README.md
@@ -1,12 +1,8 @@
 ---
 uid: S000108
-name: Stone-Čech compactification of the integers
+name: Stone-Čech compactification $\beta\omega$ of the integers
 aliases:
-  - Beta N
-  - βN
-  - Beta Z
-  - Beta omega
-  - Stone-Čech compactification of the natural numbers
+  - \beta\mathbb{N}
 counterexamples_id: 111
 refs:
   - zb: "0386.54001"

From c6a81fe35cb5a04916231a4d257f4ed422418b59 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Fri, 9 Jan 2026 23:18:07 +0100
Subject: [PATCH 3/4] typo?

---
 spaces/S000108/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/spaces/S000108/README.md b/spaces/S000108/README.md
index f3088d9a7..40b8b68dd 100644
--- a/spaces/S000108/README.md
+++ b/spaces/S000108/README.md
@@ -2,7 +2,7 @@
 uid: S000108
 name: Stone-Čech compactification $\beta\omega$ of the integers
 aliases:
-  - \beta\mathbb{N}
+  - $\beta\mathbb{N}$
 counterexamples_id: 111
 refs:
   - zb: "0386.54001"

From 951586c001fb60f1245252dc293309105b63c3f2 Mon Sep 17 00:00:00 2001
From: Patrick Rabau <70125716+prabau@users.noreply.github.com>
Date: Sat, 10 Jan 2026 00:19:31 -0500
Subject: [PATCH 4/4] minor adjustments

---
 spaces/S000108/README.md | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/spaces/S000108/README.md b/spaces/S000108/README.md
index 40b8b68dd..6da25602e 100644
--- a/spaces/S000108/README.md
+++ b/spaces/S000108/README.md
@@ -11,10 +11,11 @@ refs:
     name: Stone–Čech compactification on Wikipedia
 ---
 
-The Stone-Čech compactification of {S2}. Explicitly, $X=\beta \omega$ is the set of all ultrafilters on $\omega=\{0,1,2\dots\}$,
+The Stone-Čech compactification of {S2}.
+One way to describe $X=\beta \omega$ is as the set of all ultrafilters on $\omega=\{0,1,2\dots\}$,
 where we identify $n \in \omega$ with the principal ultrafilter containing $n$.
 The topology on $X$ is generated by all sets of the form
-$\overline U = \{F \in \beta\omega : U \in F\}$ for $U \subset \omega$.
+$\overline U = \{F \in \beta\omega : U \in F\}$ for $U \subseteq \omega$.
 
-Defined as counterexample #111 ("Stone-Cech Compactification of the Integers")
+Defined as counterexample #111 ("Stone-Čech Compactification of the Integers")
 in {{zb:0386.54001}}.