Could any one give me a hint how to show Every rational function which is holomorphic on every point

Thomas Hubbard

Thomas Hubbard

Answered question

2022-05-23

Could any one give me a hint how to show Every rational function which is holomorphic on every point of Riemann Sphere( C ) must be constant?(with out applying Maximum Modulas Theorem). Thanks.

Answer & Explanation

Mya Hurst

Mya Hurst

Beginner2022-05-24Added 13 answers

If a function is analytic on the sphere at , it is bounded in an neighborhood of . Consequently, it is bounded globally, since the complement of a neighbhorhood at is compact. Now invoke Liouville's theorem; the functon must be constant.

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