A metric space is a set with a global distance function (the metric ) that, for every two points in , gives the distance between them as a nonnegative real number . A metric space must also satisfy
1. iff ,
2. ,
3. The triangle inequality .
More things to try:
Weisstein, Eric W. "Metric Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MetricSpace.html
with a global distance function
(the metric 
) that, for every two points 
in 
, gives the distance between them
as a nonnegative real
number 
.
A metric space must also satisfy
iff 
,
,
.
