Ed Harris In addition to directing "Pollock", Harris also directed the western "Appaloosa" (2008). In television, Harris is notable for his roles as Miles Roby in the miniseries "Empire Falls" (2005) and as United States Senator John McCain in the television movie "Game Change" (2012), the latter of which earned him the Golden Globe Award for Best Supporting Actor – Series, Miniseries or Television Film. He currently stars as the Man in Black in the HBO science fiction-western series "Westworld" (2016–present), for which he earned a nomination for the Primetime Emmy Award for Outstanding Lead Actor in a Drama Series. Harris was
Directed set this article) assume that a directed set is directed upward, unless otherwise stated. Beware that other authors call a set directed if and only if it is directed both upward and downward. Directed sets are a generalization of nonempty totally ordered sets. That is, all totally ordered sets are directed sets (contrast "partially" ordered sets, which need not be directed). Join semilattices (which are partially ordered sets) are directed sets as well, but not conversely. Likewise, lattices are directed sets both upward and downward. In topology, directed sets are used to define nets, which generalize sequences and unite the various