  Let R be a perfect F_p-algebra, equipped with the trivial norm. Let W(R) be
the ring of p-typical Witt vectors over R, equipped with the p-adic norm. At
the level of nonarchimedean analytic spaces (in the sense of Berkovich), we
demonstrate a close analogy between W(R) and the polynomial ring R[T] equipped
with the Gauss norm, in which the role of the structure morphism from R to R[T]
is played by the Teichmuller map. For instance, we show that the analytic space
associated to R is a strong deformation retract of the space associated to
W(R). We also show that each fibre forms a tree under the relation of pointwise
comparison, and classify the points of fibres in the manner of Berkovich's
classification of points of a nonarchimedean disc. Some results pertain to the
study of p-adic representations of etale fundamental groups of nonarchimedean
analytic spaces (i.e., relative p-adic Hodge theory).
