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Math and science::Topology

Metric space

Metric

A metric d on a set X is a function [ d:what to what?] with the following three properties:

What is this called?
d(x,y)=0x=y, for all x,yX
Triangle inequality
[...]
Symmetry
d(x,y)=d(y,x), for all x,yX

A metric space is a set together with a metric on it, or more formally, a pair (X,d) where X is a set and d is a metric on X.