Heine–Borel in $\mathbb{R}^2$: the parabola is unbounded, the sine curve not closed

Which of the following subsets of $\mathbb{R}^2$ are not compact? (i) a circle; (ii) a parabola; (iii) $S=\{(x,y)\in\mathbb{R}^2:y=\sin\tfrac1x, 0<x\le1\}$; (iv) $T=\{(x,y)\in\mathbb{R}^2:|x|+|y|=4\}$.