Minority Report (film) Minority Report (film) Minority Report is a 2002 American neo-noir science fiction film directed by Steven Spielberg and loosely based on the short story "The Minority Report" by Philip K. Dick. It is set primarily in Washington, D.C., and Northern Virginia in the year 2054, where PreCrime, a specialized police department, apprehends criminals based on foreknowledge provided by three psychics called "precogs". The cast includes Tom Cruise as Chief of PreCrime John Anderton, Colin Farrell as Department of Justice agent Danny Witwer, Samantha Morton as the senior precog Agatha, and Max von Sydow as Anderton's superior Lamar Burgess. The film
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