  We study a simple model of p-adic closed and open strings. It sheds some
light on the dynamics of tachyon condensation for both types of strings. We
calculate the effect of static and decaying D-brane configurations on the
closed string background. For closed string tachyons we find lumps analogous to
D-branes. By studying their fluctuation spectrum and the D-branes they admit,
we argue that closed string lumps should be interpreted as spacetimes of lower
dimensionality described by some noncritical p-adic string theory.
