  We investigate refocusing and strong refocusing of light rays in a
space-time. A strongly refocusing space-time is refocusing. The converse is
unknown. We construct examples of space-times which are refocusing, but not
strongly so, at a particular point. These space-times are strongly refocusing
at other points. The geometrization conjecture proved by Perelman implies that
a globally hyperbolic refocusing space-time of dimension $\leq 4$ admits a
strongly refocusing Lorentz metric.
  We show that the possibly empty set of points at which a strongly causal
space-time is refocusing is closed. We prove that a Lorentz covering space of a
strongly causal refocusing space-time is a strongly causal refocusing
space-time. This generalizes the result of Chernov and Rudyak for globally
hyperbolic space-times.
