Math Forum :: View topic – Convergence Problem

For x in A=(1,inf), define f_n(x)=x^(1/n) Then f_n is continuous on A, and for any bounded set in A(Note: here ‘bounded set’ in A refers to those sets whose infimum is greater than 1), f_n converges uniformly, but f_n does not uniformly converge on A. Since A is homeomorphic to R, the result follows._________________Few, but ripe.

—- Carl Friedrich Gauss