Spaces with a dispersion point are not cut point spaces

theorems/T000928.md

@@ -1,15 +1,16 @@
 ---
 uid: T000928
 if:
-  and:
-  - P000045: true
-  - P000175: true
+  P000045: true
 then:
-  P000086: false
+  P000205: false
 refs:
   - mathse: 5146777
     name: Answer to "A connected space cannot have more than one dispersion point"
 ---
 
-If $|X|\ge 3$, $X$ can have at most one dispersion point.
-See Proposition 1 in {{mathse:5146777}}.
+Let $p$ be a dispersion point of $X$. If $|X|\ge 2$ and $q$ is a point distinct from $p$,
+the set $X\setminus\{q\}$ is connected by Proposition 2 in {{mathse:5146777}},
+so $q$ is not a cut point.
+And if $|X|\le 1$, $X$ has no cut point since {T558}.
+In both cases $X$ is not a {P205}.