Prove that a continuous function on $\mathbb{R}$ which is periodic attains its extreme values.
I don't know how to start this proof, but I know I have to use the extreme value theorem, continuity and something with compact sets.
2026-04-01 19:07:14.1775070434
Prove that a continuous function on $\mathbb{R}$ which is periodic attains its extreme values.
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Assume that the period equals $p$ and use the fact that the function attains all its values on, e.g., $[0,p]$, which is compact.