Fuzzy Geometry of Commutative Spaces and Quantum Dynamics

Fuzzy topology and geometry considered as the possible mathematical framework for novel quantum-mechanical formalism. In such formalism the states of massive particle m correspond to the elements of fuzzy manifold called fuzzy points. Due to the manifold weak topology, m space coordinate x acquires principal uncertainty sigma(x) and described by the positive, normalized density w((r) over right arrow, t) in 3-dimensional case. It's shown that the evolution of m state on such 3-dimensional manifold corresponds to Shroedinger dynamics of massive quantum particle.