P226 minor tweaks

Author: prabau

properties/P000226.md

@@ -6,16 +6,16 @@ refs:
     name: Finite $T_0$-spaces and universal mappings. (Holsztyński, Pedersen)
 ---
 
-A space for which every collection of open sets has a minimal element.
+Every nonempty collection of open sets has a minimal element.
 
 Equivalently:
-- Every collection of closed sets has a maximal element.
+- Every nonempty collection of closed sets has a maximal element.
 - The open sets satisfy the *descending chain condition*: There is no infinite strictly decreasing sequence $O_1 \supsetneq O_2 \supsetneq \cdots$ of open sets.
 - The closed sets satisfy the *ascending chain condition*: There is no infinite strictly increasing sequence $Y_1 \subsetneq Y_2 \subsetneq \cdots$ of closed sets.
 
 See Section 1 of {{zb:0392.54005}}.
 
-Compare this property with {P208}.
+Compare with {P208}.
 
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 #### Meta-properties