The thief is at point $(0,1)$. Before he starts to move, the police bureau of the $\mathbb{R^2}$ plain can freely place countably infinite officers along the x-axis. We know that
- The thief and the officers move simultaneously and continuously, their maximal speeds being $V_t$ and $V_o$ respectively.
- The officers are restricted to move along the x-axis. They're ghostlike and pass right through each other without collision.
- The thief and the officers are points. The thief is caught if his coordinates coincide with those of an officer.
Can the thief cross over the x-axis to the negative y hemisphere without getting caught? The answer is obvious no if $V_t\leq V_o$. But can he if $V_t\gt V_o$?
What happens if instead of occupying the x-axis, the officers occupy a circle around the thief? Can the thief break out of the circle?