1. The problem statement, all variables and given/known data Prove that (-1,1) is homeomorphic to R (real numbers), with the topology given by the usual metric. 2. Relevant equations None. 3. 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.