This construction of
as the closure of the space of the cylindrical functions of
smooth connections in the scalar product (14
) shows that
can be defined without the need of recurring to
algebraic techniques, distributional connections or the
Ashtekar-Lewandowski measure. The casual reader, however, should
be warned that the resulting
topology is different than the natural topology on the space of
connections: if a sequence
of graphs converges pointwise to a graph
, the corresponding cylindrical functions
do not converge to
in the
Hilbert space topology.