  Multidimensional cosmological model with the topology M=RxM_1xM_2x...xM_n
where M_i (i=1,... ,n) undergo a chain splitting into arbitrary number of
compact spaces is considered. It is shown that equations of motion can be
solved exactly because they depend only on the effective curvatures and
dimensions and "forget" about inner topological structure. It is proved that
effective cosmological action for the model with n=1 in the case of infinite
splitting of the internal space coincides with the tree-level effective action
for a bosonic string.
