Minority Report (film) Goldman in 1992. He created the initial script for the film with Ron Shusett and Robert Goethals (uncredited). It was supposed to be a sequel to the 1990 Dick adaptation "Total Recall", which starred Arnold Schwarzenegger. Novelist Jon Cohen was hired in 1997 to adapt the story for a potential film version that would have been directed by Dutch filmmaker Jan de Bont. Meanwhile, Cruise and Spielberg, who met and became friends on the set of Cruise's film "Risky Business" in 1983, had been looking to collaborate for ten years. Spielberg was set to direct Cruise in "Rain Man", but
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