Definition 17.1.7 (Monotone Complete).label Let $(E, \le)$ be an ordered vector space, then $E$ is monotone complete if for any order bounded directed set $A \subset E$, $\sup(A)$ exists.
Definition 17.1.7 (Monotone Complete).label Let $(E, \le)$ be an ordered vector space, then $E$ is monotone complete if for any order bounded directed set $A \subset E$, $\sup(A)$ exists.
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