  Quantum--mechanical operators corresponding to canonical momentum and
position of a point--like particle, which follow from the quantum field theory
in the general Riemannian space-time, satisfy generally to a deformation of the
canonical commutation relations with $c^{-2}$ as the parameter of deformation.
For operators of the quasi-Cartesian coordinates in the closed and open
Friedman--Robertson--Walker models, the deformation reproduces the spatial part
of the well--known Snyder formula for quantization of the Minkowsky space-time.
The spatially-flat models are distinguished apart by that the deformation is
reduced exactly to the standard canonical commutation relations, which
correlates remarkably with the fact of the observed flatness of the Universe.
Conditions are briefly discussed for which the deformation could have
cosmological manifestations. Key words: quantum mechanics, cosmology, quantized
space.
