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 While the definition of a directed set is for an "upward-directed" set (every pair of elements has an upper bound), it is also possible to define a downward-directed set in which every pair of elements has a common lower bound. A subset of a poset is downward-directed if and only if its upper closure is a filter. Directed subsets are used in domain theory, which studies directed complete partial orders. These are posets in which every upward-directed set is required to have a least upper bound. In this context, directed subsets again provide a generalization of convergent sequences. Directed set