could any one give me a hint how to show Every rational function which is holomorphic on every point of Riemann Sphere( $\mathbb{C}_{\infty}$) must be constant?(with out applying Maximum Modulas Theorem). Thank you.
Every rational function which is holomorphic on Riemann Sphere($\mathbb{C}_{\infty}$)
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riemann-surfaces
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1Does using the fact that the Riemann sphere is compact count as using the maximum modulus principle? – 2012-07-24