A characterization of pseudocompactness.
We examine when a space has a zero set universal parametrised by a metrisable space of minimal weight and show that this depends on the -weight of when is perfectly normal. We also show that if parametrises a zero set universal for then for all . We construct zero set universals that have nice properties (such as separability or ccc) in the case where the space has a -coarser topology. Examples are given including an space with zero set universal parametrised by an space (and...