B. Gunther, A COMPACTUM THAT CANNOT BE AN ATTRACTOR OF A SELF-MAP ON A MANIFOLD, Proceedings of the American Mathematical Society, 120(2), 1994, pp. 653-655
A one-dimensional compactum (in fact, a certain solinoid) is construct
ed, such that there does not exist a self-map on a manifold having thi
s compactum as attractor.