Ed Harris Wilkinson in "" (2007), alongside Nicolas Cage. In 2008, he co wrote, directed and starred along with Viggo Mortensen in the western Appaloosa. In 2010, he and wife Amy Madigan appeared together in Ash Adams' independent crime drama "Once Fallen". Later that same year, Harris starred in the survival drama "The Way Back" as Mr. Smith. His performance received much critical praise, and he was suggested by critics to receive a fifth Oscar nomination. In 2012, he co-starred alongside Sam Worthington in the thriller film "Man on a Ledge" for Summit Entertainment. He then won the Golden Globe Award for
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