_Northrop Nortronics_
_Systems Support Department_
_Anaheim, California_
It is shown that by the use of Information
Theory, any metrizable topology may be metrized
as an orthogonal Euclidean space (with a random
Gaussian probability distribution) times
a denumerable random cartesian product of
irreducible (wrt direct product) denumerable
groups. The necessary algorithm to accomplish
this metrization from a statistical basis is
presented. If such a basis is unavailable,
a certain nilpotent projection operator has
to be used instead, as is shown in detail in
the companion paper. This operator possesses
self-organizing features.