The metric topology on a metric space 
is the topology induced by its
metric 
. The open sets are all subsets that can be realized as the
unions of open balls
 |
where 
,
and 
.
The metric topology makes 
a T2-space.
Given two distinct points 
and 
of 
, their distance 
is certainly positive, so the open balls 
and 
are disjoint neighborhoods of 
and 
, respectively.
