Abstract
The notion of dual uniformity is introduced on
, the uniform space of uniformly continuous mappings between
and
, where
and
are two uniform spaces. It is shown that a function space uniformity on
is admissible (resp. splitting) if and only if its dual uniformity on
is admissible (resp. splitting). It is also shown that a uniformity on
is admissible (resp. splitting) if and only if its dual uniformity on
is admissible (resp. splitting). Using duality theorems, it is also proved that the greatest splitting uniformity and the greatest splitting family open uniformity exist on
and
, respectively, and these two uniformities are mutually dual splitting uniformities.