Universal ultrametric spaces of smallest weight
A. Lemin and V. Lemin proved that every ultrametric space of weight at most $\tau$ can be isometricaly embedded into their ultrametric space $LW_\tau^\prime$. We show that every ultrametric space of weight at most $\tau^\omega$ can be isometricaly embedded into their ultrametric space $LW_\tau^\prime$. This provided a solution to a problem raised by the A. Lemin.