I have thought of two curves and I'm wondering if they are closed. $\gamma_1(t)=(\sin t,0,0)$ and $\gamma_2(t)=(t-\left \lfloor{t}\right \rfloor ,0,0)$. Intuitively, I think they should both be closed, but I'm worried about issues of smoothness/domain. Does it make a difference if I consider the domain to be $\mathbb{R}$, $[0,2\pi)$, or $[0,2\pi)$?
2026-03-26 17:13:34.1774545214
Are these curves closed in the following domains?
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