Given 
metric spaces 
, with metrics 
respectively, the product
metric 
is a metric on the Cartesian
product 
defined as
 |
This definition can be extended to the product of countably many metric spaces.
If for all 
,
and 
is the Euclidean metric
of the real line, the product metric induces the Euclidean topology of the 
-dimensional Euclidean space 
. It does not coincide with the Euclidean metric of 
, but it is equivalent to it.
