  This report introduces and investigates a family of metrics on sets of
pointed Kripke models. The metrics are generalizations of the Hamming distance
applicable to countably infinite binary strings and, by extension, logical
theories or semantic structures. We first study the topological properties of
the resulting metric spaces. A key result provides sufficient conditions for
spaces having the Stone property, i.e., being compact, totally disconnected and
Hausdorff. Second, we turn to mappings, where it is shown that a widely used
type of model transformations, product updates, give rise to continuous maps in
the induced topology.
