We show that for $U$ and $V$ balanced open subsets of (Qno) Fr\'echet spaces $E$ and $F$ that we have the topological identity $$ \bigl( {\cal H}(U\times V), \tau_\omega \bigr) = \biggl( {\cal H} \Bigl( U; \bigl( {\cal H}(V), \tau_\omega \bigr) \Bigr), \tau_\omega \biggr). $$ Analogous results for the compact open topology have long been established. We also give an example to show that the (Qno) hypothesis on both $E$ and $F$ is necessary.

This paper deals with the projective objects in the category of all $Z$-frames, where the latter is a common generalization of different types of frames. The main result obtained here is that a $Z$-frame is ${\bf E}$-projective if and only if it is stably $Z$-continuous, for a naturally arising collection ${\bf E}$ of morphisms.