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 this setting, a subset "A" of a partially ordered set ("P",≤) is called a directed subset if it is a directed set according to the same partial order: in other words, it is not the empty set, and every pair of elements has an upper bound. Here the order relation on the elements of "A" is inherited from "P"; for this reason, reflexivity and transitivity need not be required explicitly. A directed subset of a poset is not required to be downward closed; a subset of a poset is directed if and only if its downward closure is an ideal.