If X is a compact, locally connected metric space, f : X → X is a homeomorphism, and Q is a closed neighborhood of X, then Z = {p ∈ Q : f(p) ∈ Q for all integers n} is the permanent set for f on Q, and E = {p ∈ Q : there is some positive integer Np such that if n ≥ Np, then f−n(p) ∈ Q} is the entrainment set. In a previous paper, we began a study of the entrainment sets of topological horseshoe...

This paper deals with directly indecomposable direct factors of a directed set.

The topic of indecomposable finite-dimensional representations of the Poincaré group was first studied in a systematic way by S. Paneitz ([5][6]). In these investigations only representations with one source were considered, though by duality, one representation with 2 sources was implicitly present. The idea of nilpotency was mentioned indirectly in Paneitz’s articles, but a more down-to-earth...