  Some known relativistic paradoxes are reconsidered for closed spaces, using a
simple geometric model. For two twins in a closed space, a real paradox seems
to emerge when the traveling twin is moving uniformly along a geodesic and
returns to the starting point without turning back. Accordingly, the reference
frames (RF) of both twins seem to be equivalent, which makes the twin paradox
irresolvable: each twin can claim to be at rest and therefore to have aged more
than the partner upon their reunion. In reality, the paradox has the resolution
in this case as well. Apart from distinction between the two RF with respect to
actual forces in play, they can be distinguished by clock synchronization. A
closed space singles out a truly stationary RF with single-valued global time;
in all other frames, time is not a single-valued parameter. This implies that
even uniform motion along a spatial geodesic in a compact space is not truly
inertial, and there is an effective force on an object in such motion.
Therefore, the traveling twin will age less upon circumnavigation than the
stationary one, just as in flat space-time. Ironically, Relativity in this case
emerges free of paradoxes at the price of bringing back the pre-Galilean
concept of absolute rest.
  An example showing the absence of paradoxes is also considered for a more
realistic case of a time-evolving closed space.
