M.C.Abbati, A.Mania`
On Differential Structure for Projective Limits of Manifolds
(179K, Latex 2e)

ABSTRACT.  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 ${\cal C}^\infty$ calculus proposed by Fr\"ohlicher 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.