Vaughn's point is a good one, but not quite apropos of Tom's notion of self-similarity. In the category of ordered sets the final co-algebra of the Pavlovic-Pratt functor is, indeed, the half-open real interval, [0,1). But Tom was in the category of topological spaces. To make [0,1) into a self-similar _space_ one must reinterpret their functor so that the new point of the one-point compactification of each copy of X is identified with the bottom of the next copy. So what interesting space was first described as the final co-algebra of a functor? (I think that locution succeeds in avoiding such things as constant functors.) I would suggest the one-point compactification of the countable discrete set. (The functor, of course, is 1 + X.) Peter 24-Nov-2004 20:03:48 -0400,2672;000000000000-00000000