Which of the following subsets of $ \mathbb{R^2}$ are compact?
$\displaystyle \{(x, y) : xy = 1\}$
$\displaystyle \{(x, y) : x^{\large\frac{2}{3}} + y^{\large\frac{2}{3}} = 1\}$
$\displaystyle \{(x, y) : x^2 + y^2 < 1\}$
I am stuck on this problem. Can anyone help me please?