  The chain relation, due to Conley, and the strong chain relation, due to
Easton, are well studied for continuous maps on compact metric spaces.
Following Fathi and Pageault, we use barrier functions to generalize the theory
to general relations on uniform spaces. In developing the theory, we indicate
why the chain ideas are naturally uniform spaces concepts. We illustrate that
the extension to relations is easy and is useful even for the study of the
continuous map case.

Dynamical Systems