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 Directed set In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set "A" together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound. In other words, for any "a" and "b" in "A" there must exist "c" in "A" with "a" ≤ "c" and "b" ≤ "c". The notion defined above is sometimes called an upward directed set. A downward directed set is defined analogously, meaning when every pair of elements is bounded below. Some authors (and