How do you show that a doubly-periodic continuous function $f:\Bbb C→\Bbb C$ is bounded?
2026-03-30 22:52:57.1774911177
Periodic continuous functions are bounded using complex analysis
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The result is not true unless you mean doubly-periodic instead of periodic.
If that is what you mean, then here is a hint:
A continuous function on a compact subset of $\mathbb{C}$ is bounded (and attains its minimum and maximum).
The values of a doubly-periodic function are all equal to the values on some initial parallelogram containing the origin.