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

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10 changes: 5 additions & 5 deletions spaces/S000108/README.md
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Original file line number Diff line number Diff line change
@@ -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"
Expand All @@ -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")
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