  Social dynamics models may present discontinuities in the right-hand side of
the dynamics for multiple reasons, including topology changes and quantization.
Several concepts of generalized solutions for discontinuous equations are
available in the literature and are useful to analyze these models. In this
chapter, we study Caratheodory and Krasovsky generalized solutions for
discontinuous models of opinion dynamics with state dependent interactions. We
consider two definitions of "bounded confidence" interactions, which we
respectively call metric and topological: in the former, individuals interact
if their opinions are closer than a threshold; in the latter, individuals
interact with a fixed number of nearest neighbors. We compare the dynamics
produced by the two kinds of interactions, in terms of existence, uniqueness
and asymptotic behavior of different types of solutions.
