Update T000550.md

theorems/T000550.md

@@ -8,4 +8,5 @@ then:
  P000146: true
 ---
 
-In a {P39} space $X$, every nonempty open set is dense, so to admit a shrinking, every open cover must contain $X$. Thus, any open cover admits a clopen refinement.
+In a {P39} space $X$, the closure of every nonempty open set is $X$, so any open cover that admits a shrinking must contain $X$ (as otherwise each of its open sets could only contain the closure of $\varnothing$).
+Thus, any such open cover admits an open refinement to the partition $\{X\}$.