- #1

- 801

- 70

## Homework Statement

Prove that (-1,1) is homeomorphic to R (real numbers), with the topology given by the usual metric.

## Homework Equations

None.

## The Attempt at a Solution

I constructed the function f(x) = [1/(1-x) - 1/(1+x)]/2 = x/[(1+x)(1-x)] which is continuous and maps (-1,1) to R. Next I need to show that f has a continuous inverse. I'm stuck here.