  A topological crossover, associated with the collapse of the Fermi surface in
strongly correlated Fermi systems, is examined. It is demonstrated that in
these systems, the temperature domain where standard Fermi liquid results hold
dramatically narrows, because the Landau regime is replaced by a classical one.
The impact of the collapse of the Fermi surface on pairing correlations is
analyzed. In the domain of the Lifshitz phase diagram where the Fermi surface
collapses, splitting of the BCS superconducting phase transition into two
different ones of the same symmetry is shown to occur.
