This was the original paper that introduced the successor representation, in the context of linear function approximation in discrete, finite MDPs where we can describe transitions using transition matrices. This was 1993, remember, so we didn't need to cram text into pages and have detailed plots, but it also means the description and context is usually less clear.
The application is a maze with a barrier, but all I get out of this is that the SR can tell us that states close to each other but on opposite sides of a mze are actually "distant" in feature representation. But I don't see how this improves generalization, and that's what I wanted to understand from this paper.
I'm having a hard time understanding what this paper is trying to say, unfortunately.