Update spaces/S000209/properties/P000216.md

Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com>

Author: felixpernegger

spaces/S000209/properties/P000216.md

@@ -4,4 +4,9 @@ property: P000216
 value: true
 ---
 
-Similar to {S83|P216}, using that {S170|P216}.
+It is enough to show that each open set in $X$ is {P30}.
+The whole space is {P30} since {S209|P16}.
+And a proper open subset of $X$ is a disjoint union of open sets,
+each homeomorphic to either {S25} or {S83}.
+Both {S25|P30} and {S83|P30}.
+Since the {P30} property is perserved by taking disjoint unions, the result follows.