Metric Space

Definition

A metric space is an ordered pair $(M,d)$ where $M$ is a set and $d$ is a metric on $M$.

$$d:M\times M\to \mathbb{R}$$

1. $d(x,x)=0$

2. $d(x,y)>0,x\ne y$

3. $d(x,y)=d(y,x)$

4. $d(x,z)\le d(x,y)+d(y,z)$