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 notions of limit used in analysis. Directed sets also give rise to direct limits in abstract algebra and (more generally) category theory. In addition to the definition above, there is an equivalent definition. A directed set is a set "A" with a preorder such that every finite subset of "A" has an upper bound. In this definition, the existence of an upper bound of the empty subset implies that "A" is nonempty. Examples of directed sets include: Directed sets are a more general concept than (join) semilattices: every join semilattice is a directed set, as the join or least upper