  (This short article is a continuation of a longer, review work, in the same
volume of Proceedings, by Ashtekar, Marolf and Mour\~ao [gr-qc/9403042]. All
the details and other results are to be found in joint papers of the author
with Abhay Ashtekar.) The projective limit technics derived for spaces of
connections are extended to a new framework which for the associated projective
limit plays a role of the differential geometry. It provides us with powerfull
technics for construction and studding various operators. In particular, we
introduce the commutator algebra of `vector fields', define a divergence of a
vector field and find for them a quantum representation. Among the vector
fields, there are operators which we identify as regularised Rovelli-Smolin
loop operators linear in momenta. Another class of operators which comes out
naturally are Laplace operators.
