  We construct a theory of quantum fluctuatons in a regular array of small
superconductive islands connected via low-resistance tunnel contacts to a dirty
thin metal film.
  Electron-electron interaction in the film is assumed to be repulsive. The
system is macroscopically superconductive when the distance between
neighbouring islands is short enough. The zero-temperature phase transition
from superconductive to normal-conductive state is shown to occur with the
increase of distance between superconductive islands; the logarithm of the
critical distance is proportional to the low-frequency zero-voltage Andreev
conductance between the SC island and the film. This critical distance is
always much less the than the two-dimensional localization length, so the
considered effect develops when weak-localization corrections are still small.
The dependence of the critical temperature on the film conductance and
inter-island distance is found.
