  In "Rips complexes and covers in the uniform category" \cite{Rips} the
authors define, following James \cite{J}, covering maps of uniform spaces and
introduce the concept of generalized uniform covering maps. Conditions for the
existence of universal uniform covering maps and generalized uniform covering
maps are given. This paper extends these results by investigating the existence
of these covering maps relative to subgroups of the uniform fundamental group
and the fundamental group of the base space.
