  Function space topologies are developed for EC(Y,Z), the class of
equi-continuous mappings from a topological space Y to a uniform space Z.
Properties such as splittingness, admissibility etc. are defined for such
spaces. The net theoretic investigations are carried out to provide
characterizations of splittingness and admissibility of function spaces on
EC(Y,Z). The open-entourage topology and point-transitive-entourage topology
are shown to be admissible and splitting respectively. Dual topologies are
defined. A topology on EC(Y,Z) is found to be admissible (resp. splitting) if
and only if its dual is so.
