Improve definition Stone-Cech compactification of the integers (S108) (#1571)

Author: felixpernegger

spaces/S000108/README.md

@@ -1,12 +1,8 @@
 ---
 uid: S000108
-name: Stone-Cech compactification of the integers
+name: Stone-Čech compactification $\beta\omega$ of the integers
 aliases:
-  - Beta N
-  - βN
-  - Beta Z
-  - Beta omega
-  - Stone-Cech compactification of the natural numbers
+  - $\beta\mathbb{N}$
 counterexamples_id: 111
 refs:
   - zb: "0386.54001"
@@ -15,10 +11,11 @@ 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
-$\overline U = \{F \in \beta\omega : U \in F\}$ for $U \subset \omega$.
+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 $U \subseteq \omega$.
 
-Defined as counterexample #111 ("Stone-Cech Compactification of the Integers")
+Defined as counterexample #111 ("Stone-Čech Compactification of the Integers")
 in {{zb:0386.54001}}.