T553 update: hereditarily connected => locally contractible

Author: prabau

spaces/S000221/properties/P000230.md

@@ -3,7 +3,8 @@ uid: T000553
 if:
   P000196: true
 then:
-  P000042: true
+  P000223: true
 ---
 
-Every subset of a {P196} space is {P40}, and {T38}.
+Since {T585}, every nonempty subset of $X$ is also {P199}.
+In particular, every open neighborhood of every point is {P199}.