The Virasoro algebra with $c=1$ has a continuum of superselection sectors characterized by the ground state energy h. Only a discrete subset of sectors arises by restriction of representations of the $SU(2)$ current algebra at level $k=1$. The remaining continuum of sectors is obtained with the help of (localized) homomorphisms into the current algebra. The fusion product of continuum sectors with discrete sectors is computed. A new method of determining the sector of a state is used.