  We show that the tropicalization of an irreducible d-dimensional variety over
a field of characteristic 0 is (d-l)-connected through codimension one, where l
is the dimension of the lineality space of the tropicalization. From this we
obtain a higher connectivity result for skeleta of rational polytopes. We also
prove a tropical analogue of the Bertini Theorem: the intersection of the
tropicalization of an irreducible variety with a generic hyperplane is again
the tropicalization of an irreducible variety.
