  Fuzzy geometry considered as the possible mathematical framework for
reformulation of quantum-mechanical formalism in geometric terms. In this
approach the states of massive particle m correspond to elements of fuzzy
manifold called fuzzy points. In 1-dimensional case, due to manifold ultraweak
(fuzzy) topology, m space coordinate x acquires principal uncertainty dx and
described by positive, normalized density w(x,t). Analogous uncertainties
appear for fuzzy point on 3-dimensional manifold. It's shown that m states on
such manifold are equivalent to vectors (rays) on complex Hilbert space, their
evolution correspond to Shroedinger dynamics of nonrelativistic quantum
particle.
