  The purely mathematical root of the dequantization constructions is the quest
for a sheafification needed for presheaves on a noncommutative space. The
moment space is constructed as a commutative space, approximating the
noncommutative space appearing as a dynamical space, via a stringwise
construction. The main result phrased is purely mathematical, i.e. the
noncommutative stalks of some sheaf on the noncommutative space can be
identified to stalks of some sheaf associated to it on the commutative geometry
(topology) of the moment space. This may be seen as a (partial) inverse to the
deformation--quantization idea, but in fact with a much more precise behaviour
of stalks of sheaves. The method, based on minimal axiomatics necessary to
rephrase continuity principles in terms of partial order (noncommutative
topology) exclusively, leads to the appearance of objects like strings and
(M--)branes. Also, spectral families and observables may be defined and studied
as separated filtrations on the noncommutative topology! We highlight the
relation with pseudo--places and generalized valuation theory. Finally, we hint
at a new notion of ``space'' as a dynamical system of noncommutative topologies
with the same commutative shadow (4 dimensional space--time if you wish) and
variable (but isomorphic) moment spaces, which for special choices may be
thought of as a higher dimensional brane--space.
