  We prove that in a closed manifold of dimension between 3 and 7 with a bumpy
metric, the min-max minimal hypersurfaces associated with the volume spectrum
introduced by Gromov, Guth, Marques-Neves, are two-sided and have multiplicity
one. This confirms a conjecture by Marques-Neves.
  We prove that in a bumpy metric each volume spectrum is realized by the
min-max value of certain relative homotopy class of sweepouts of boundaries of
Caccioppoli sets. The main result follows by approximating such min-max value
using the min-max theory for hypersurfaces with prescribed mean curvature
established by the author with Zhu.
