  Dodson-Zeeman fuzzy topology considered as the possible mathematical
framework of quantum geometric formalism. In such formalism the states of
massive particle m correspond to elements of fuzzy manifold called fuzzy
points. Due to their weak (partial) ordering, m space coordinate x acquires
principal uncertainty dx. It's shown that m evolution with minimal number of
additional assumptions obeys to schroedinger and dirac formalisms in
norelativistic and relativistic cases correspondingly. It's argued that
particle's interactions on such fuzzy manifold should be gauge invariant.
