  In this note we discuss the possibility to define a space-time with a DSR
based approach. We show that the strategy of defining a non linear realization
of the Lorentz symmetry with a consistent vector composition law cannot be
reconciled with the extra request of an invariant length (time) scale. The
latter request forces to abandon the group structure of the translations and
leaves a space-time structure where points with relative distances smaller or
equal to the invariant scale can not be unambiguously defined.
