  We continue our earlier investigation of dp-finite fields. We show that the
"heavy sets" of [6] are exactly the sets of full dp-rank. As a consequence,
full dp-rank is a definable property in definable families of sets. If $I$ is
the group of infinitesimals, we show that $1 + I$ is the group of
multiplicative infinitesimals. From this, we deduce that the canonical topology
is a field topology. Lastly, we consider the (unlikely) conjecture that the
canonical topology is a V-topology. Assuming this conjecture, we deduce the
classification of dp-finite fields conjectured by Halevi, Hasson, and Jahnke.
