better first lines for properties with multiple characterizations

properties/P000090.md

@@ -11,9 +11,10 @@ aliases:
 - Alexandroff-discrete
 ---
 
-Any of the following equivalent properties holds:
+An arbitrary intersection of open sets is open.
+
+This is equivalent to each of the following:
 
-* An arbitrary intersection of open sets is open.
 * An arbitrary union of closed sets is closed.
 * Each $x \in X$ has a unique smallest neighborhood.
 * For each $A \subseteq X$, $A$ is open iff $A \cap Y$ is open in the subspace $Y$ for each finite $Y \subseteq X$.

properties/P000185.md

@@ -8,9 +8,10 @@ refs:
   name: On ultrapseudocompact and related spaces (T. Nieminen)
 ---
 
-Any of the following equivalent properties holds:
+There exists a basis for the topology that is also a partition into disjoint sets.
+
+This is equivalent to each of the following:
 
-- There exists a basis for the topology that is also a partition into disjoint sets.
 - Every open set is closed.
 - Every closed set is open.
 - The space's Kolmogorov quotient is {P52}.

properties/P000195.md

@@ -13,9 +13,10 @@ refs:
   name: Stone space on Wikipedia
 ---
 
-Any of the following equivalent properties holds:
+The space is {P16}, {P3}, and {P47}.
+
+This is equivalent to each of the following:
 
-- The space is {P16}, {P3}, and {P47}.
 - The space is {P16} and {P48}.
 - The space is {P16}, {P1}, and {P50}.
 - The space is {P75} and {P2}.

properties/P000196.md

@@ -8,9 +8,10 @@ refs:
   name: On ultrapseudocompact and related spaces (T. Nieminen)
 ---
 
-Any of the following equivalent properties holds:
+Every subspace is connected.
+
+This is equivalent to each of the following:
 
-- Any subspace is connected.
 - The open sets are totally ordered by inclusion.
 - The closed sets are totally ordered by inclusion.
 - The specialization preorder is total.