  We consider the correlation functions in a gas of electrons moving within a
thin layer on the surface of nanosize sphere. A closed form of expressions for
the RKKY indirect exchange, superconducting Cooper loop and `density-density'
correlation function is obtained. The systematic comparison with planar results
is made, the effects of spherical geometry are outlined. The quantum coherence
of electrons leads to the enhancement of all correlations for the
points--antipodes on the sphere. This effect is lost when the radius of the
sphere exceeds the temperature coherence length.
