- #1
madness
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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.