  We show that every topological factoring between two zero dimensional
dynamical systems can be represented by a sequence of morphisms between the
levels of the associated ordered Bratteli diagrams. Conversely, we will prove
that given an ordered Bratteli diagram $B$ with a continuous Vershik map on it,
every sequence of morphisms between levels of $B$ and $C$, where $C$ is another
ordered Bratteli diagram with continuous Vershik map, induces a topological
factoring if and only if $B$ has a unique infinite min path. We present a
method to construct various examples of ordered premorphisms between two
decisive Bratteli diagrams such that the induced maps between the two Vershik
systems are not topological factorings. We provide sufficient conditions for
the existence of a topological factoring from an ordered premorphism. Expanding
on the modelling of factoring, we generalize the Curtis-Hedlund-Lyndon theorem
to represent factor maps between two zero dimensional dynamical systems through
sequences of sliding block codes.
