  According to the Anderson theorem, the critical temperature T_c of a
disordered superconductor is determined by the average density of states and
does not change at the localization threshold. This statement is valid under
assumption of a self-averaging order parameter, which can be violated in the
strong localization region. Stimulating by statements on the essential increase
of T_c near the Anderson transition, we carried out the systematic
investigation of possible violations of self-averaging. Strong deviations from
the Anderson theorem are possible due to resonances at the quasi-discrete
levels, resulting in localization of the order parameter at the atomic scale.
This effect is determined by the properties of individual impurities and has no
direct relation to the Anderson transition. In particular, we see no reasons to
say on "fractal superconductivity" near the localization threshold.
