# Talk:Closed Set in Linearly Ordered Space

Would it be better to state this more like "If $s$ is a supremum of $S$, then $s \in Y$"? --Dfeuer (talk) 07:40, 12 February 2013 (UTC)
$Y$ is closed in $X$ iff: for each nonempty $S \subseteq Y$, if $b \in X$ is a supremum or infimum of $S$ then $b \in Y$.