  We develop Conley's theory for multivalued maps on finite topological spaces.
More precisely, for discrete-time dynamical systems generated by the iteration
of a multivalued map which satisfies appropriate regularity conditions, we
establish the notions of isolated invariant sets and index pairs, and use them
to introduce a well-defined Conley index. In addition, we verify some of its
fundamental properties such as the Wazewski property and continuation.
