| [ Teach ] in KIDS 글 쓴 이(By): rosedale (언제쯤...) 날 짜 (Date): 1997년06월16일(월) 11시06분45초 KDT 제 목(Title): [re] 복소 문제.. 그 문제는요.. 제 기억이 맞다면 silverman책에 있는 문제인것 같군요.. :) pole이 isolated singularity이기 때문에 limit point는 essential singularity 같은 놈이 되어야지. pole이 될수는 없겠죠.... 만약 limit point z_0 가 pole이 된다면 충분히 작은 nbhd를 잡아도, singularity를 주는 z_n이 존재하겠죠.. 뭐 이건 그냥 개념적인거구.. 좀더 formal하게 설명하자면.. Suppose f has a pole of order k at z_0. Let g(z) = (z-z_0)^k g(z). Then g has pole at each z_n and g(z_0) can be defined. ( because, pole is a removable singularity.) Hence, for sufficiently small nbhd of z_0, g is bounded. However, the convergence of the sequence (z_n) implies that z_n is contains the nbhd of z_0 for sufficiently large n. This leads to a contradiction. |