A topology induced by the metric 
defined on a metric
space 
.
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.
