  It is well-known that quasi-one-dimensional superconductors suffer from the
pairing fluctuations that significantly reduce the superconducting temperature
or even completely suppress any coherent behavior. Here we demonstrate that a
coupling to a robust pair condensate changes the situation dramatically. In
this case the quasi-one-dimensional system can be a high temperature
superconductor governed by the proximity to the Lifshitz transition at which
the Fermi level approaches the lower edge of the single-particle spectrum.
