Following earlier work by E.Maillet 100 years ago, we introduce the
definition of a Liouville set, which extends the definition of a Liouville
number. We also define a Liouville field, which is a field generated by a
Liouville set. Any Liouville number belongs to a Liouville set S having the
power of continuum and such that the union of S with the rational number field
is a Liouville field.Comment: Proceedings of the American Mathematical Society, to appea