In summary, the original metrizable topological space was decomposed
into an orthogonal Euclidean space times[21] a denumerable random
cartesian product of irreducible (wrt direct product) denumerable
groups. Thus, since any individual component of a random cartesian
product may be studied independently of the others, all that one needs
to study is: (1) a Gaussian distribution on a single real axis and (2)
the irreducible denumerable groups.
[21] Random cartesian product.
Finally, it should be emphasized that there are only these two ways
of decomposing a metrizable topology; (1) if a (statistical) basis
is given, use the diagonalization of a symmetric matrix algorithm
described earlier (and given in detail in the three channels in cascade
problem), and (2) otherwise use a suitable network of the NPO’s with
n₀=1. Of course, any hybrid of these two methods may be employed as
well.