  We investigate the topological properties of Berkovich analytifications over
hybrid fields, that is a field equipped with the maximum of its native norm and
the trivial norm. We prove that the analytification of the affine line or of a
smooth projective curve over a countable Archimedean hybrid field is
contractible, and show that it can be non-contractible when the field is
uncountable. Further, we prove that the analytification of affine space over a
non-Archimedean hybrid field or over a discrete valuation ring is contractible.
As an application, we show that the Berkovich affine line over the ring of
integers of a number field is contractible.
