Exercise 9, § 2

Let $E$ be a Riesz space, $\Omega$ the space of relatively bounded linear forms on $E$. Consider the topology on $\Omega$ defined by the semi-norms $L \mapsto |L|(x)$, where $x$ runs over the set of elements $\geqslant 0$ of $E$. Show that $\Omega$, equipped with this topology, is Hausdorff and complete.