Complex Analysis: Theory and Applications · Problem 7.1.7

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · uniform-convergence

Problem

Suppose that the sequences of functions {fn}\{f_n\} and {gn}\{g_n\} converge uniformly on the set TT. ((a)) Show that the sequence {fn+gn}\{f_n + g_n\} converges uniformly on TT. ((b)) Show by example that it is not necessarily the case that {fngn}\{f_n g_n\} converges uniformly on TT.

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