Let $L^{\varphi }$ be an Orlicz space defined by a convex Orlicz function $\varphi$ and let $E^{\varphi }$ be the space of finite elements in $L^{\varphi }$ (= the ideal of all elements of order continuous norm). We show that the usual norm topology ${𝒯}_{\varphi }$ on $L^{\varphi }$ restricted to $E^{\varphi }$ can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear operators defined on $E^{\varphi }$.

Given two topologies, $T_1$ and $T_2$, on the same set X, the intersection topologywith respect to $T_1$ and $T_2$ is the topology with basis $U_1\cap U_2:U_1\in T_1,U_2\in T_2$. Equivalently, T is the join of $T_1$ and $T_2$ in the lattice of topologies on the set X. Following the work of Reed concerning intersection topologies with respect to the real line and the countable ordinals, Kunen made an extensive investigation of normality, perfectness and ${\omega }_1$-compactness in this class of topologies. We demonstrate that the majority of his results generalise...