A uniformly discrete metric space is a metric space 
with a constant 
such that
 |
for every pair of distinct points. For example, 
with Euclidean distance
is uniformly discrete. The subset 
of 
has isolated points but
fails this uniform condition. Bounded geometry
additionally bounds the number of points in balls
of each fixed radius. These conditions enter the coarse
Novikov conjecture and the definitions of Roe algebras.
