  Generalized uncertainty principle and breakdown of the spacetime continuum
certainly represent two important results derived of various approaches related
to quantum gravity and black hole physics near the well-known Planck scale. The
discreteness of space suggests, in particular, that all measurable lengths are
quantized in units of a fundamental scale (in this case, the Planck length).
Here, we propose a self-consistent theoretical framework for an important class
of physical systems characterized by a finite space of states, and show that
such a framework enlarges previous knowledge about generalized uncertainty
principles, as topological effects in finite-dimensional discrete phase spaces
come into play. Besides, we also investigate under what circumstances the
generalized uncertainty principle (GUP) works out well and its inherent
limitations.
