I think by intuition that the periodic function over the entire real line must be boundary. But I do not know how to prove it. If the function is continuous, the I can just choose a closed intervel of a period and it has obviously boundary. But when the function is not that great I have no idea in how to prove it. Or if that is not true, could you give an counterexample?
2026-03-18 11:50:21.1773834621
Is periodic function over the entire $\mathbf{R}$ necessarily boundary
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