  The paper analyzes dynamic epistemic logic from a topological perspective.
The main contribution consists of a framework in which dynamic epistemic logic
satisfies the requirements for being a topological dynamical system thus
interfacing discrete dynamic logics with continuous mappings of dynamical
systems. The setting is based on a notion of logical convergence,
demonstratively equivalent with convergence in Stone topology. Presented is a
flexible, parametrized family of metrics inducing the latter, used as an
analytical aid. We show maps induced by action model transformations continuous
with respect to the Stone topology and present results on the recurrent
behavior of said maps.
