The coarse uniform convergence
space is one which is the coarsest member of its convergence class. Each convergence
space is compatible with a coarse uniform convergence structure. The regular
topological spaces can be characterized as those whose coarse uniform convergence
structures are uniformly regular or, equivalently, as those convergence spaces whose
coarse uniform convergence structures are very strongly bounded. Every coarse
uniform convergence space has a coarse completion. The coarse uniform convergence
spaces which have uniformly regular completions are precisely the coarse uniform
spaces.
