T552 fix

theorems/T000552.md

@@ -8,4 +8,4 @@ if:
 then:
  P000129: true
 ---
-Any clopen partition of a {P36} space $X$ must contain $X$, so to admit clopen refinements every open cover must contain $X$. Thus, the union of all open sets except for $X$ cannot equal $X$ (as that would be an open cover not containing $X$), so some points have $X$ as their only neighborhood. By homogeneity, this must then be true of all points, i.e. the space is {P129}.
+Any clopen partition of a {P36} space $X$ must contain $X$, so every open cover admitting a clopen partition as refinement must contain $X$. Thus, the union of all open sets except for $X$ cannot equal $X$ (as that would be an open cover not containing $X$), so some points have $X$ as their only neighborhood. By homogeneity, this must then be true of all points, i.e. the space is {P129}.