  We study $b$-property of a sublattice (or an order ideal) $F$ of a vector
lattice $E$. In particular, $b$-property of $E$ in $E^\delta$, the Dedekind
completion of $E$, $b$-property of $E$ in $E^u$, the universal completion of
$E$, and $b$-property of $E$ in $\hat{E}(\hat{\tau})$, the completion of $E$.
