  We investigate the differential calculus defined by Ashtekar and Lewandowski
on projective limits of manifolds by means of cylindrical smooth functions and
compare it with the C^infty calculus proposed by Froehlicher and Kriegl in more
general context. For products of connected manifolds, a Boman theorem is
proved, showing the equivalence of the two calculi in this particular case.
Several examples of projective limits of manifolds are discussed, arising in
String Theory and in loop quantization of Gauge Theories.
