  We investigate affine Berkovich spaces over maximally complete fields and
prove that they may be approximated by simpler spaces when the only functions
we need to evaluate are polynomials of bounded degree. We derive applications
to semi-algebraic sets and recover a result of E. Hrushovski and F. Loeser
which claims that points of Berkovich spaces give rise to definable types (a
model-theoretic notion of tameness).
