The French metro metric is an example for disproving apparently intuitive but false properties of metric spaces. The metric consists
of a distance function on the plane such that for all 
,
 |
(1)
|
where 
is the normal distance function on the plane. This metric has the property that for
,
the open ball of radius 
around 
is an open line segment along vector 
, while for 
, the open ball is the
union of a line segment and an open disk around the
origin.
