DEF-TOP. Top and Bottom.
Let $(X,\leq)$ be a preordered set and let $a\in X$.
$a$ is a top of $X$, if
\[\forall x\in X : x\leq a.\]$a$ is a bottom of $Y$, if
\[\forall x\in X : a\leq x.\]
DEF-TOP. Top and Bottom.
Let $(X,\leq)$ be a preordered set and let $a\in X$.
$a$ is a top of $X$, if
\[\forall x\in X : x\leq a.\]$a$ is a bottom of $Y$, if
\[\forall x\in X : a\leq x.\]