Let $P = (X, {\preceq})$ be a D1103: Partially ordered set.
The set of upper bounds of $E \subseteq X$ with respect to $P$ is the D11: Set \begin{equation} \{ m \in X \mid \forall \, x \in E : (x, m) \in {\preceq} \} \end{equation}

Let $P = (X, {\preceq})$ be a D1103: Partially ordered set.
The set of upper bounds of $E \subseteq X$ with respect to $P$ is the D11: Set \begin{equation} \{ m \in X \mid \forall \, x \in E : x \preceq m \} \end{equation}