Top and Bottom

🅟 Feb 22, 2026

  🅤 Feb 22, 2026

Set Theory > Orders

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

    \[\forall x\in X : a\leq x.\]