Compact universals

A Tychonoff space X has a zero-set or an open regular Fσ universal parametrised by a σ-compact space if and only if X is metrisable. Weakening the condition to the parametrising space being Lindelöf-Σ implies that X is strongly quasi-developable. as an open Fσ universal parametrised by a σ-compact space then X is developable. In this case if the parametrising space is Lindelöf-Σ then X has a quasi-development. Some examples are given.