  We consider Farey series of rational numbers in terms of {\it fractal sets}
labeled by the Hausdorff dimension with values defined in the interval 1$ $$ <
$$ $$h$$ $$ <$$ $$ 2$ and associated with fractal curves. Our results come from
the observation that the fractional quantum Hall effect-FQHE occurs in pairs of
{\it dual topological quantum numbers}, the filling factors. These quantum
numbers obey some properties of the Farey series and so we obtain that {\it the
universality classes of the quantum Hall transitions are classified in terms of
$h$}. The connection between Number Theory and Physics appears naturally in
this context.
