# Could someone specify a metric on (0,1)

1. Feb 11, 2013

### Bachelier

could someone specify a metric on (0,1) that defines (the same topology) as the abs. value (i.e. usual) metric and makes this open interval into a complete set?

Thanks

2. Feb 11, 2013

### micromass

Staff Emeritus
Re: Homeomorphism

There is a homeomorphism $T:(0,1)\rightarrow \mathbb{R}$. Pull back the metric from $\mathbb{R}$. Thus define

$$d(x,y)= |T(x)-T(y)|$$