Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2009 / 4 / i / a

For closed sets in $\mathbb{R}$, the answers are $X_1$: no; $X_2$: yes; $X_3$: yes. The first interval omits its limit point zero. The second contains its finite limit points, and the empty set is closed in every topology.